1/2!+2/3!+3/4!+.+n/（n+1）!

1/2!+2/3!+3/4!+.+n/（n+1）!
1/2!+2/3!+3/4!+.+n/（n+1）!

1/2!+2/3!+3/4!+.+n/（n+1）!
n/(n+1)!=1/n!-1/(n+1)!
Sn=1-1/(n+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)!

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)!能详细点吗？刚学这个。。。。哪里没理解？ n/(n+1)! = (n...

全部展开

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)!

收起

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！