1/2!+2/3!+…+n/(n+1) n趋于无穷大时的极限怎么求?
问题描述：
1/2!+2/3!+…+n/(n+1) n趋于无穷大时的极限怎么求?
错了。最后是 n/(n+1)!
答
设每一项为An,和为Sn,可猜想Sn=[(n+1)!-1]/(n+1)!因为S2=[(2+1)!-1]/(2+1),假设Sn=[(n+1)!-1]/(n+1)!,则S(n+1)=Sn+(n+1)/(n+2)!=[(n+1)!-1]/(n+1)!+(n+1)/(n+2)!=[(n+2)!-1]/(n+2)!=1-1/(n+2)!所以极限为1...