1/2! + 2/3! + 3/4! + ... + 99/100!
(where 100! = 1 * 2 * 3 * 4 * ... * 99 * 100 )
What is the sum
2009-12-11 8:12 pm
回答 (1)
2009-12-11 9:00 pm
✔ 最佳答案
考慮通項 : n / (n + 1)! = [(n + 1) - 1] / (n + 1)!
= (n + 1) / (n + 1)! - 1 / (n + 1)!
= 1 / n! - 1 / (n + 1)!
因此 :
1/2! + 2/3! + 3/4! +...+ 99/100!
=(1/1! - 1/2!) + (1/2! - 1/3!) + (1/3! - 1/4!) + ... + (1/99! - 1/100!)
= 1/1! - 1/100!
= 1 - 1/100!
參考: 052
收錄日期: 2021-04-21 22:05:11
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091211000051KK00431