summation問題

2011-05-21 12:59 am
請問點解 e^x = summation of x^i / i! from i=0 to infinity?
希望有人可以解釋一下!Thank you!
更新1:

Re AnAnd: 咩事呀 = =

回答 (1)

2011-05-21 6:18 am
✔ 最佳答案
e^x = Σ(i = 0 to infinity) x^i / i!
= 1 + x + x^2 / 2! + x^3 / 3! + x^4 / 4! + ...

By definition,
e^x = lim_(i->infinity) (1 + x/i)^i
= 1 + x + x^2 / 2! + x^3 / 3! + x^4 / 4! + ...

which is equal to Σ(i = 0 to infinity) x^i / i!
參考: Knowledge is power.


收錄日期: 2021-04-25 17:04:26
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110520000051KK00595

檢視 Wayback Machine 備份