[中學] 分母是階乘的計算

看板Math作者 (5566)時間13年前 (2012/09/16 23:25), 編輯推噓3(3推 0噓 10→)
留言13則, 6人參與, 最新討論串1/1
請問 1+1/2!-1/3!+1/4!.... 有公式解嗎? 謝謝!!!!!! -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 180.177.105.253
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09/16 23:27, , 1F
1/3!是-還是+
09/16 23:27, 1F
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09/16 23:28, , 2F
e定義為1+1/1!+1/2!+1/3!+1/4!+1/5!+... (是超越數)
09/16 23:28, 2F
推
09/16 23:30, , 3F
1+e^(-1)
09/16 23:30, 3F
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09/16 23:32, , 4F
正負相間
09/16 23:32, 4F
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09/16 23:32, , 5F
那我打錯了...
09/16 23:32, 5F
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09/16 23:33, , 6F
應該是1-1/2!+1/3!-1/4!.....
09/16 23:33, 6F
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09/16 23:36, , 7F
那就是1-e^(-1)啦.看e^x那泰勒展開就有答案嚕
09/16 23:36, 7F
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09/16 23:37, , 8F
那請如果是1+1/2!-1/3!+1/n!呢??
09/16 23:37, 8F
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09/16 23:38, , 9F
更正 1+1/2!-1/3!.....+1/n!
09/16 23:38, 9F
推
09/17 22:21, , 10F
.....有更正嗎
09/17 22:21, 10F
推
09/18 08:30, , 11F
e^(-1)=1-1/1!+1/2!-1/3!+...這樣給你了比較容易補吧
09/18 08:30, 11F
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08/13 17:05, , 12F
e定義為1+1/1!+ https://noxiv.com
08/13 17:05, 12F
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09/17 15:00, , 13F
//noxiv.com https://daxiv.com
09/17 15:00, 13F
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文章代碼(AID): #1GLU-1us (Math)