{"id":7736,"date":"2020-08-14T15:22:43","date_gmt":"2020-08-14T08:22:43","guid":{"rendered":"https:\/\/witpoko.com\/?p=7736"},"modified":"2020-08-14T15:22:43","modified_gmt":"2020-08-14T08:22:43","slug":"%e0%b8%a7%e0%b8%b4%e0%b8%97%e0%b8%a2%e0%b9%8c%e0%b8%a1-%e0%b8%95%e0%b9%89%e0%b8%99-zenos-paradoxes-infinite-series-%e0%b9%80%e0%b8%a5%e0%b9%88%e0%b8%99%e0%b8%81%e0%b8%b1%e0%b8%9a%e0%b8%84","status":"publish","type":"post","link":"https:\/\/witpoko.com\/?p=7736","title":{"rendered":"\u0e27\u0e34\u0e17\u0e22\u0e4c\u0e21.\u0e15\u0e49\u0e19: Zeno&#8217;s Paradoxes, Infinite Series, \u0e40\u0e25\u0e48\u0e19\u0e01\u0e31\u0e1a\u0e04\u0e27\u0e32\u0e21\u0e40\u0e09\u0e37\u0e48\u0e2d\u0e22"},"content":{"rendered":"\n<p>\u0e27\u0e31\u0e19\u0e19\u0e35\u0e49\u0e40\u0e23\u0e32\u0e04\u0e38\u0e22\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07\u0e40\u0e2b\u0e25\u0e48\u0e32\u0e19\u0e35\u0e49\u0e01\u0e31\u0e19\u0e04\u0e23\u0e31\u0e1a<\/p>\n\n\n\n<p>1. \u0e1c\u0e21\u0e1e\u0e39\u0e14\u0e04\u0e38\u0e22\u0e01\u0e31\u0e1a\u0e40\u0e14\u0e47\u0e01\u0e46\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07\u0e04\u0e27\u0e32\u0e21\u0e40\u0e09\u0e37\u0e48\u0e2d\u0e22 \u0e41\u0e25\u0e30\u0e40\u0e14\u0e47\u0e01\u0e46\u0e44\u0e14\u0e49\u0e17\u0e33\u0e01\u0e34\u0e08\u0e01\u0e23\u0e23\u0e21\u0e40\u0e01\u0e35\u0e48\u0e22\u0e27\u0e01\u0e31\u0e1a\u0e04\u0e27\u0e32\u0e21\u0e40\u0e09\u0e37\u0e48\u0e2d\u0e22\u0e40\u0e2b\u0e21\u0e37\u0e2d\u0e19\u0e43\u0e19\u0e04\u0e25\u0e34\u0e1b<a rel=\"noreferrer noopener\" href=\"https:\/\/witpoko.com\/?p=7723\" target=\"_blank\">\u0e17\u0e35\u0e48\u0e25\u0e34\u0e07\u0e01\u0e4c\u0e19\u0e35\u0e49<\/a>\u0e04\u0e23\u0e31\u0e1a<\/p>\n\n\n\n<p>2. \u0e1c\u0e21\u0e40\u0e25\u0e48\u0e32\u0e43\u0e2b\u0e49\u0e40\u0e14\u0e47\u0e01\u0e46\u0e1f\u0e31\u0e07\u0e27\u0e48\u0e32\u0e41\u0e23\u0e07\u0e42\u0e19\u0e49\u0e21\u0e16\u0e48\u0e27\u0e07\u0e14\u0e36\u0e07\u0e43\u0e2b\u0e49\u0e14\u0e27\u0e07\u0e14\u0e32\u0e27\u0e42\u0e04\u0e08\u0e23\u0e01\u0e31\u0e19\u0e40\u0e1b\u0e47\u0e19\u0e27\u0e07\u0e23\u0e35 \u0e43\u0e2b\u0e49\u0e40\u0e14\u0e47\u0e01\u0e46\u0e14\u0e39\u0e41\u0e1a\u0e1a\u0e08\u0e33\u0e25\u0e2d\u0e07\u0e17\u0e35\u0e48 <a rel=\"noreferrer noopener\" href=\"https:\/\/scratch.mit.edu\/projects\/225919898\/\" target=\"_blank\">Newtonian Orbit<\/a> \u0e41\u0e25\u0e30 <a rel=\"noreferrer noopener\" href=\"https:\/\/scratch.mit.edu\/projects\/227691459\/\" target=\"_blank\">Dance of Comets<\/a> \u0e17\u0e35\u0e48\u0e40\u0e1b\u0e47\u0e19\u0e42\u0e1b\u0e23\u0e41\u0e01\u0e23\u0e21\u0e20\u0e32\u0e29\u0e32 Scratch<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/pAKNUWytRCc?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-US&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><figcaption> \u0e2b\u0e19\u0e49\u0e32\u0e15\u0e32 Dance of Comets \u0e40\u0e1b\u0e47\u0e19\u0e1b\u0e23\u0e30\u0e21\u0e32\u0e13\u0e19\u0e35\u0e49\u0e04\u0e23\u0e31\u0e1a<\/figcaption><\/figure>\n\n\n\n<p>3. \u0e1c\u0e21\u0e22\u0e01\u0e15\u0e31\u0e27\u0e2d\u0e22\u0e48\u0e32\u0e07 <a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Zeno%27s_paradoxes\" target=\"_blank\">Zeno&#8217;s Paradox<\/a> \u0e21\u0e32\u0e2b\u0e19\u0e36\u0e48\u0e07\u0e2d\u0e31\u0e19\u0e04\u0e37\u0e2d\u0e16\u0e49\u0e32\u0e40\u0e23\u0e32\u0e08\u0e30\u0e40\u0e14\u0e34\u0e19\u0e17\u0e32\u0e07\u0e08\u0e32\u0e01\u0e08\u0e38\u0e14 A \u0e44\u0e1b\u0e08\u0e38\u0e14 B \u0e40\u0e23\u0e32\u0e15\u0e49\u0e2d\u0e07\u0e40\u0e14\u0e34\u0e19\u0e17\u0e32\u0e07\u0e44\u0e1b\u0e04\u0e23\u0e36\u0e48\u0e07\u0e17\u0e32\u0e07\u0e01\u0e48\u0e2d\u0e19 \u0e41\u0e25\u0e49\u0e27\u0e01\u0e47\u0e40\u0e14\u0e34\u0e19\u0e17\u0e32\u0e07\u0e44\u0e1b\u0e2d\u0e35\u0e01\u0e04\u0e23\u0e36\u0e48\u0e07\u0e17\u0e32\u0e07\u0e02\u0e2d\u0e07\u0e17\u0e35\u0e48\u0e40\u0e2b\u0e25\u0e37\u0e2d \u0e41\u0e25\u0e49\u0e27\u0e01\u0e47\u0e40\u0e14\u0e34\u0e19\u0e17\u0e32\u0e07\u0e44\u0e1b\u0e2d\u0e35\u0e01\u0e04\u0e23\u0e36\u0e48\u0e07\u0e17\u0e32\u0e07\u0e02\u0e2d\u0e07\u0e17\u0e35\u0e48\u0e40\u0e2b\u0e25\u0e37\u0e2d \u0e2d\u0e22\u0e48\u0e32\u0e07\u0e19\u0e35\u0e49\u0e44\u0e1b\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e22\u0e46\u0e44\u0e21\u0e48\u0e23\u0e39\u0e49\u0e08\u0e1a \u0e41\u0e25\u0e49\u0e27\u0e17\u0e33\u0e44\u0e21\u0e40\u0e23\u0e32\u0e16\u0e36\u0e07\u0e40\u0e14\u0e34\u0e19\u0e17\u0e32\u0e07\u0e08\u0e32\u0e01 A \u0e44\u0e1b B \u0e44\u0e14\u0e49 \u0e23\u0e30\u0e22\u0e30\u0e17\u0e32\u0e07\u0e17\u0e35\u0e48\u0e40\u0e14\u0e34\u0e19\u0e23\u0e27\u0e21\u0e46\u0e01\u0e31\u0e19\u0e08\u0e30\u0e40\u0e1b\u0e47\u0e19\u0e40\u0e17\u0e48\u0e32\u0e44\u0e23 \u0e1e\u0e2d\u0e40\u0e14\u0e47\u0e01\u0e46\u0e07\u0e07\u0e2a\u0e31\u0e01\u0e1e\u0e31\u0e01\u0e40\u0e23\u0e32\u0e01\u0e47\u0e25\u0e2d\u0e07\u0e1a\u0e27\u0e01\u0e23\u0e30\u0e22\u0e30\u0e17\u0e32\u0e07\u0e01\u0e31\u0e19 \u0e42\u0e14\u0e22\u0e43\u0e2b\u0e49\u0e23\u0e30\u0e22\u0e30\u0e17\u0e32\u0e07\u0e08\u0e32\u0e01 A \u0e16\u0e36\u0e07 B \u0e40\u0e17\u0e48\u0e32\u0e01\u0e31\u0e1a 1 \u0e2b\u0e19\u0e48\u0e27\u0e22 \u0e23\u0e30\u0e22\u0e30\u0e17\u0e32\u0e07\u0e17\u0e31\u0e49\u0e07\u0e2b\u0e21\u0e14\u0e17\u0e35\u0e48\u0e40\u0e14\u0e34\u0e19\u0e01\u0e47\u0e04\u0e37\u0e2d 1\/2 + 1\/4 + 1\/8 + 1\/16 + 1\/32 + &#8230; <br><br>\u0e40\u0e14\u0e47\u0e01\u0e46\u0e25\u0e2d\u0e07\u0e1a\u0e27\u0e01\u0e43\u0e19\u0e2a\u0e40\u0e1b\u0e23\u0e14\u0e0a\u0e35\u0e15\u0e08\u0e30\u0e44\u0e14\u0e49\u0e04\u0e33\u0e15\u0e2d\u0e1a\u0e40\u0e17\u0e48\u0e32\u0e01\u0e31\u0e1a 1 \u0e16\u0e32\u0e21 <a rel=\"noreferrer noopener\" href=\"https:\/\/www.wolframalpha.com\/input\/?i=1%2F2+%2B+1%2F4+%2B+1%2F8+%2B+1%2F16+%2B+...\" target=\"_blank\">Wolfram Alpha<\/a> \u0e01\u0e47\u0e44\u0e14\u0e49\u0e04\u0e33\u0e15\u0e2d\u0e1a\u0e40\u0e17\u0e48\u0e32\u0e01\u0e31\u0e1a 1 \u0e41\u0e25\u0e30\u0e1c\u0e21\u0e41\u0e2a\u0e14\u0e07\u0e27\u0e34\u0e18\u0e35\u0e17\u0e33\u0e14\u0e49\u0e27\u0e22\u0e21\u0e37\u0e2d\u0e01\u0e47\u0e44\u0e14\u0e49\u0e04\u0e33\u0e15\u0e2d\u0e1a\u0e40\u0e17\u0e48\u0e32\u0e01\u0e31\u0e1a 1<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"921\" height=\"1024\" data-attachment-id=\"7737\" data-permalink=\"https:\/\/witpoko.com\/?attachment_id=7737\" data-orig-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?fit=2144%2C2384&amp;ssl=1\" data-orig-size=\"2144,2384\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Screen-Shot-2563-08-14-at-14.52.30\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?fit=921%2C1024&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?resize=921%2C1024&#038;ssl=1\" alt=\"\" class=\"wp-image-7737\" srcset=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?resize=921%2C1024&amp;ssl=1 921w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?resize=270%2C300&amp;ssl=1 270w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?resize=768%2C854&amp;ssl=1 768w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?resize=1381%2C1536&amp;ssl=1 1381w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?resize=1842%2C2048&amp;ssl=1 1842w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.52.30.jpg?w=2000&amp;ssl=1 2000w\" sizes=\"auto, (max-width: 921px) 100vw, 921px\" \/><figcaption>\u0e43\u0e2b\u0e49  <a rel=\"noreferrer noopener\" href=\"https:\/\/www.wolframalpha.com\/input\/?i=1%2F2+%2B+1%2F4+%2B+1%2F8+%2B+1%2F16+%2B+...\" target=\"_blank\">Wolfram Alpha \u0e2b\u0e32\u0e04\u0e48\u0e32\u0e02\u0e2d\u0e07 1\/2 + 1\/4 + 1\/8 + &#8230; <\/a>\u0e43\u0e2b\u0e49\u0e04\u0e23\u0e31\u0e1a<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"990\" height=\"960\" data-attachment-id=\"7738\" data-permalink=\"https:\/\/witpoko.com\/?attachment_id=7738\" data-orig-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.55.17.jpg?fit=990%2C960&amp;ssl=1\" data-orig-size=\"990,960\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Screen-Shot-2563-08-14-at-14.55.17\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.55.17.jpg?fit=990%2C960&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.55.17.jpg?resize=990%2C960&#038;ssl=1\" alt=\"\" class=\"wp-image-7738\" srcset=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.55.17.jpg?w=990&amp;ssl=1 990w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.55.17.jpg?resize=300%2C291&amp;ssl=1 300w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/Screen-Shot-2563-08-14-at-14.55.17.jpg?resize=768%2C745&amp;ssl=1 768w\" sizes=\"auto, (max-width: 990px) 100vw, 990px\" \/><figcaption>\u0e04\u0e33\u0e19\u0e27\u0e13 1\/2 + 1\/4 + 1\/8 + 1\/16 + &#8230; \u0e14\u0e49\u0e27\u0e22\u0e21\u0e37\u0e2d \u0e15\u0e31\u0e49\u0e07\u0e0a\u0e37\u0e48\u0e2d\u0e43\u0e2b\u0e49\u0e1c\u0e25\u0e23\u0e27\u0e21\u0e04\u0e37\u0e2d S \u0e41\u0e25\u0e49\u0e27\u0e2b\u0e32\u0e27\u0e48\u0e32 S \u0e15\u0e49\u0e2d\u0e07\u0e21\u0e35\u0e04\u0e48\u0e32\u0e40\u0e17\u0e48\u0e32\u0e44\u0e23<\/figcaption><\/figure>\n\n\n\n<p>4. \u0e04\u0e27\u0e32\u0e21\u0e08\u0e23\u0e34\u0e07\u0e2a\u0e34\u0e48\u0e07\u0e17\u0e35\u0e48\u0e40\u0e23\u0e32\u0e2a\u0e19\u0e43\u0e08\u0e04\u0e37\u0e2d\u0e40\u0e23\u0e32\u0e2a\u0e32\u0e21\u0e32\u0e23\u0e16\u0e40\u0e04\u0e25\u0e37\u0e48\u0e2d\u0e19\u0e17\u0e35\u0e48\u0e08\u0e32\u0e01 A \u0e44\u0e1b B \u0e44\u0e14\u0e49\u0e44\u0e2b\u0e21 \u0e40\u0e23\u0e32\u0e08\u0e36\u0e07\u0e04\u0e27\u0e23\u0e14\u0e39\u0e27\u0e48\u0e32\u0e40\u0e23\u0e32\u0e43\u0e0a\u0e49\u0e40\u0e27\u0e25\u0e32\u0e40\u0e17\u0e48\u0e32\u0e44\u0e23\u0e43\u0e19\u0e01\u0e32\u0e23\u0e40\u0e04\u0e25\u0e37\u0e48\u0e2d\u0e19\u0e17\u0e35\u0e48\u0e08\u0e32\u0e01 A \u0e44\u0e1b B \u0e2a\u0e21\u0e21\u0e38\u0e15\u0e34\u0e27\u0e48\u0e32\u0e40\u0e23\u0e32\u0e40\u0e04\u0e25\u0e37\u0e48\u0e2d\u0e19\u0e17\u0e35\u0e48\u0e14\u0e49\u0e27\u0e22\u0e04\u0e27\u0e32\u0e21\u0e40\u0e23\u0e47\u0e27\u0e04\u0e07\u0e17\u0e35\u0e48 v \u0e40\u0e27\u0e25\u0e32\u0e17\u0e35\u0e48\u0e43\u0e0a\u0e49\u0e17\u0e31\u0e49\u0e07\u0e2b\u0e21\u0e14\u0e01\u0e47\u0e04\u0e37\u0e2d 1\/(2v) + 1\/(4v) + 1\/(8v) + &#8230; \u0e0b\u0e36\u0e48\u0e07\u0e40\u0e17\u0e48\u0e32\u0e01\u0e31\u0e1a 1\/v \u0e40\u0e1b\u0e47\u0e19\u0e40\u0e27\u0e25\u0e32\u0e17\u0e35\u0e48\u0e40\u0e1b\u0e47\u0e19\u0e44\u0e1b\u0e44\u0e14\u0e49\u0e16\u0e49\u0e32 v \u0e21\u0e35\u0e04\u0e48\u0e32\u0e40\u0e1b\u0e47\u0e19\u0e1a\u0e27\u0e01<\/p>\n\n\n\n<p>5. \u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07\u0e1b\u0e23\u0e30\u0e2b\u0e25\u0e32\u0e14\u0e17\u0e35\u0e48\u0e40\u0e14\u0e47\u0e01\u0e46\u0e44\u0e14\u0e49\u0e40\u0e2b\u0e47\u0e19\u0e27\u0e31\u0e19\u0e19\u0e35\u0e49\u0e04\u0e37\u0e2d\u0e16\u0e49\u0e32\u0e40\u0e23\u0e32\u0e1a\u0e27\u0e01\u0e2d\u0e30\u0e44\u0e23\u0e40\u0e02\u0e49\u0e32\u0e44\u0e1b\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e22\u0e46\u0e44\u0e21\u0e48\u0e21\u0e35\u0e17\u0e35\u0e48\u0e2a\u0e34\u0e49\u0e19\u0e2a\u0e38\u0e14 \u0e1a\u0e32\u0e07\u0e17\u0e35\u0e1c\u0e25\u0e23\u0e27\u0e21\u0e01\u0e47\u0e40\u0e1b\u0e47\u0e19\u0e15\u0e31\u0e27\u0e40\u0e25\u0e02\u0e17\u0e35\u0e48\u0e40\u0e23\u0e32\u0e23\u0e39\u0e49\u0e08\u0e31\u0e01\u0e16\u0e49\u0e32\u0e2a\u0e34\u0e48\u0e07\u0e17\u0e35\u0e48\u0e40\u0e23\u0e32\u0e1a\u0e27\u0e01\u0e40\u0e02\u0e49\u0e32\u0e44\u0e1b\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e22\u0e46\u0e21\u0e35\u0e02\u0e19\u0e32\u0e14\u0e40\u0e25\u0e47\u0e01\u0e25\u0e07\u0e40\u0e23\u0e47\u0e27\u0e1e\u0e2d \u0e40\u0e0a\u0e48\u0e19 1\/2 + 1\/4 + 1\/8 + &#8230; = 1 \u0e2b\u0e23\u0e37\u0e2d 1\/3 + 1\/9 + 1\/27 + 1\/81 + &#8230; = 1\/2 \u0e2b\u0e23\u0e37\u0e2d 1 + 2\/3 + (2\/3)^2 + (2\/3)^3 +&#8230; = 3<br><br>6. \u0e41\u0e15\u0e48\u0e16\u0e49\u0e32\u0e2a\u0e34\u0e48\u0e07\u0e17\u0e35\u0e48\u0e40\u0e23\u0e32\u0e1a\u0e27\u0e01\u0e40\u0e02\u0e49\u0e32\u0e44\u0e1b\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e22\u0e46\u0e44\u0e21\u0e48\u0e40\u0e25\u0e47\u0e01\u0e25\u0e07\u0e40\u0e23\u0e47\u0e27\u0e1e\u0e2d \u0e1c\u0e25\u0e23\u0e27\u0e21\u0e01\u0e47\u0e2d\u0e32\u0e08\u0e44\u0e21\u0e48\u0e21\u0e35\u0e04\u0e48\u0e32\u0e41\u0e19\u0e48\u0e19\u0e2d\u0e19 \u0e2d\u0e32\u0e08\u0e42\u0e15\u0e44\u0e21\u0e48\u0e08\u0e33\u0e01\u0e31\u0e14 \u0e40\u0e0a\u0e48\u0e19 1 + 1\/2 + 1\/3 + 1\/4 + &#8230; \u0e08\u0e30\u0e21\u0e35\u0e02\u0e19\u0e32\u0e14\u0e44\u0e21\u0e48\u0e08\u0e33\u0e01\u0e31\u0e14<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"641\" height=\"1024\" data-attachment-id=\"7739\" data-permalink=\"https:\/\/witpoko.com\/?attachment_id=7739\" data-orig-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2221.jpeg?fit=1001%2C1600&amp;ssl=1\" data-orig-size=\"1001,1600\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1597378115&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"IMG_2221\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2221.jpeg?fit=641%2C1024&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2221.jpeg?resize=641%2C1024&#038;ssl=1\" alt=\"\" class=\"wp-image-7739\" srcset=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2221.jpeg?resize=641%2C1024&amp;ssl=1 641w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2221.jpeg?resize=188%2C300&amp;ssl=1 188w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2221.jpeg?resize=768%2C1228&amp;ssl=1 768w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2221.jpeg?resize=961%2C1536&amp;ssl=1 961w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2221.jpeg?w=1001&amp;ssl=1 1001w\" sizes=\"auto, (max-width: 641px) 100vw, 641px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"679\" height=\"1024\" data-attachment-id=\"7740\" data-permalink=\"https:\/\/witpoko.com\/?attachment_id=7740\" data-orig-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2222.jpeg?fit=1061%2C1600&amp;ssl=1\" data-orig-size=\"1061,1600\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1597378115&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"IMG_2222\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2222.jpeg?fit=679%2C1024&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2222.jpeg?resize=679%2C1024&#038;ssl=1\" alt=\"\" class=\"wp-image-7740\" srcset=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2222.jpeg?resize=679%2C1024&amp;ssl=1 679w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2222.jpeg?resize=199%2C300&amp;ssl=1 199w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2222.jpeg?resize=768%2C1158&amp;ssl=1 768w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2222.jpeg?resize=1019%2C1536&amp;ssl=1 1019w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2222.jpeg?w=1061&amp;ssl=1 1061w\" sizes=\"auto, (max-width: 679px) 100vw, 679px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"797\" data-attachment-id=\"7741\" data-permalink=\"https:\/\/witpoko.com\/?attachment_id=7741\" data-orig-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2224.jpeg?fit=1600%2C1246&amp;ssl=1\" data-orig-size=\"1600,1246\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1597378179&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"IMG_2224\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2224.jpeg?fit=1024%2C797&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2224.jpeg?resize=1024%2C797&#038;ssl=1\" alt=\"\" class=\"wp-image-7741\" srcset=\"https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2224.jpeg?resize=1024%2C797&amp;ssl=1 1024w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2224.jpeg?resize=300%2C234&amp;ssl=1 300w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2224.jpeg?resize=768%2C598&amp;ssl=1 768w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2224.jpeg?resize=1536%2C1196&amp;ssl=1 1536w, https:\/\/i0.wp.com\/witpoko.com\/wp-content\/uploads\/2020\/08\/IMG_2224.jpeg?w=1600&amp;ssl=1 1600w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p>7. \u0e40\u0e14\u0e47\u0e01\u0e46\u0e17\u0e14\u0e25\u0e2d\u0e07\u0e1a\u0e27\u0e01\u0e40\u0e25\u0e02\u0e1e\u0e27\u0e01\u0e19\u0e35\u0e49\u0e17\u0e31\u0e49\u0e07\u0e43\u0e19\u0e2a\u0e40\u0e1b\u0e23\u0e14\u0e0a\u0e35\u0e15 \u0e41\u0e25\u0e30\u0e17\u0e14\u0e25\u0e2d\u0e07<a href=\"https:\/\/www.wolframalpha.com\/input\/?i=1+%2B+1%2F2+%2B+1%2F3+%2B+1%2F4+%2B+...+\" target=\"_blank\" rel=\"noreferrer noopener\">\u0e16\u0e32\u0e21 Wolfram Alpha<\/a> \u0e14\u0e39 \u0e15\u0e31\u0e27\u0e2d\u0e22\u0e48\u0e32\u0e07\u0e2a\u0e40\u0e1b\u0e23\u0e14\u0e0a\u0e35\u0e15\u0e21\u0e35<a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1TEjIUIRrGnlNxTeDOt_h49qdmruQ2BH3njR68LnrWfU\/edit?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">\u0e17\u0e35\u0e48\u0e19\u0e35\u0e48<\/a>\u0e41\u0e25\u0e30<a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1COYTWWJXHUZIBzcXJK-nr9Zn0TJymLOQlWvsI_Orreg\/edit?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">\u0e17\u0e35\u0e48\u0e19\u0e35\u0e48<\/a>\u0e04\u0e23\u0e31\u0e1a<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0e27\u0e31\u0e19\u0e19\u0e35\u0e49\u0e40\u0e23\u0e32\u0e04\u0e38\u0e22\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07\u0e40\u0e2b\u0e25\u0e48\u0e32\u0e19\u0e35\u0e49\u0e01\u0e31\u0e19\u0e04\u0e23\u0e31\u0e1a 1. \u0e1c\u0e21\u0e1e\u0e39\u0e14\u0e04\u0e38\u0e22\u0e01\u0e31\u0e1a\u0e40\u0e14\u0e47\u0e01\u0e46\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07\u0e04\u0e27\u0e32\u0e21\u0e40\u0e09\u0e37\u0e48\u0e2d\u0e22 \u0e41\u0e25\u0e30\u0e40\u0e14\u0e47\u0e01\u0e46\u0e44\u0e14\u0e49\u0e17\u0e33\u0e01\u0e34\u0e08\u0e01\u0e23\u0e23\u0e21\u0e40\u0e01\u0e35\u0e48\u0e22\u0e27\u0e01\u0e31\u0e1a\u0e04\u0e27\u0e32\u0e21\u0e40\u0e09\u0e37\u0e48\u0e2d\u0e22\u0e40\u0e2b\u0e21\u0e37\u0e2d\u0e19\u0e43\u0e19\u0e04\u0e25\u0e34\u0e1b\u0e17\u0e35\u0e48\u0e25\u0e34\u0e07\u0e01\u0e4c\u0e19\u0e35\u0e49\u0e04\u0e23\u0e31\u0e1a 2. \u0e1c\u0e21\u0e40\u0e25\u0e48\u0e32\u0e43\u0e2b\u0e49\u0e40\u0e14\u0e47\u0e01\u0e46\u0e1f\u0e31\u0e07\u0e27\u0e48\u0e32\u0e41\u0e23\u0e07\u0e42\u0e19\u0e49\u0e21\u0e16\u0e48\u0e27\u0e07\u0e14\u0e36\u0e07\u0e43\u0e2b\u0e49\u0e14\u0e27\u0e07\u0e14\u0e32\u0e27\u0e42\u0e04\u0e08\u0e23\u0e01\u0e31\u0e19\u0e40\u0e1b\u0e47\u0e19\u0e27\u0e07\u0e23\u0e35 \u0e43\u0e2b\u0e49\u0e40\u0e14\u0e47\u0e01\u0e46\u0e14\u0e39\u0e41\u0e1a\u0e1a\u0e08\u0e33\u0e25\u0e2d\u0e07\u0e17\u0e35\u0e48 Newtonian Orbit \u0e41\u0e25\u0e30 Dance of Comets \u0e17\u0e35\u0e48\u0e40\u0e1b\u0e47\u0e19\u0e42\u0e1b\u0e23\u0e41\u0e01\u0e23\u0e21\u0e20\u0e32\u0e29\u0e32 Scratch 3. &hellip; <a title=\"\u0e27\u0e34\u0e17\u0e22\u0e4c\u0e21.\u0e15\u0e49\u0e19: Zeno&#8217;s Paradoxes, Infinite Series, \u0e40\u0e25\u0e48\u0e19\u0e01\u0e31\u0e1a\u0e04\u0e27\u0e32\u0e21\u0e40\u0e09\u0e37\u0e48\u0e2d\u0e22\" class=\"hm-read-more\" href=\"https:\/\/witpoko.com\/?p=7736\"><span class=\"screen-reader-text\">\u0e27\u0e34\u0e17\u0e22\u0e4c\u0e21.\u0e15\u0e49\u0e19: Zeno&#8217;s Paradoxes, Infinite Series, \u0e40\u0e25\u0e48\u0e19\u0e01\u0e31\u0e1a\u0e04\u0e27\u0e32\u0e21\u0e40\u0e09\u0e37\u0e48\u0e2d\u0e22<\/span>Read 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