己知 e=∞Σn=0 (1/n!)
1+1/2!+1/3!+1/4!+...=e-1 (唔知呢條有冇用,唔需要既可以唔洗理佢)
1+3/1!+5/2!+7/3!+...=∞Σn=0 (2n+1)/n!
證明1+3/1!+5/2!+7/3!+...=3e
唔該大家幫下手
數學m1難題
2010-09-22 2:09 am
回答 (1)
2010-09-22 2:51 am
✔ 最佳答案
1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ... = e 1/1! + 2/2! + 3/3! + 4/4! + 5/5! + ... = e 2/1! + 4/2! + 6/3! + 8/4! + 10/5! + ... = 2e(2/1! + 4/2! + 6/3! + 8/4! + 10/5! + ...) + (1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ... ) = 2e + e
1/0! + 3/1! + 5/2! + 7/3! + 9/4!... = 3e
收錄日期: 2021-04-13 17:32:22
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100921000051KK00908