求(1⼀2的阶乘+2⼀3的阶乘+。。。+n⼀(n+1)的阶乘)的极限

2025-02-27 08:28:09
推荐回答(1个)
回答1:

n/(n+1)!=1/n!-1/(n+1)!,
(1/2的阶乘+2/3的阶乘+。。。+n/(n+1)的阶乘)=1/n!-1/(n+1)!+1/(n-1)!-1/n!+...
+1/2!-1/3!+1/1!-1/2!=1-1/(n+1)!
故(1/2的阶乘+2/3的阶乘+。。。+n/(n+1)的阶乘)的极限为1.