1/2!+2/3!+3/4!+.+n/（n+1）!

网友回答

n/(n+1)!=1/n!-1/(n+1)!
Sn=1-1/(n+1)!
======以下答案可供参考======
供参考答案1:
k/(k+1)!=(k+1)/(k+1)!-1/(k+1)!=1/k!-1/(k+1)!
所以原式=1/1-1/2!+1/2!-1/3!+...+1/n!-1/(n+1)!
=1-1/(n+1)!
供参考答案2:
n/(n+1)! = (n+1-1) / (n+1)! = 1/n! - 1/(n+1)!
原式 = (1/1! - 1/2!) + (1/2! - 1/3!) + (1/3! - 1/4!) + ... + [1/n!-1/(n+1)!]
= 1/1! - 1/(n+1)!
= 1 - 1/(n+1)!
供参考答案3:
首先通项n/（n+1）！= [(n+1)-1]/（n+1）！=(n+1)//（n+1）！-1/（n+1）！=1/n！-1/（n+1）！
然后1/2！=1-1/2！
2/3！=1/2！-1/3！
3/4！=1/3！-1/4！
...再然后，你懂的！