设Sn是级数∑2^[1/(n+1)]-2^(1/n)的前n项和 则lim(n→无穷大)Sn=_______
问题描述:
设Sn是级数∑2^[1/(n+1)]-2^(1/n)的前n项和 则lim(n→无穷大)Sn=_______
无穷级数是从1到无穷大
答
Sn = 2^(1/2)-2^(1/1) + 2^(1/3)-2^(1/2) + . +2^(1/n)-2^【1/(n-1】+ 2^[1/(n+1)]-2^(1/n)
= -2^(1/1) + 2^[1/(n+1)]
则lim(n→无穷大)Sn=-1