lim 1-2+3-4+...+(2n-1)-2n/ n -1=多少

题目

lim 1-2+3-4+...+(2n-1)-2n/ n -1=多少
如题

答案

先看分子 是两个等差数列的和
{1,3,5,7,9……2n-1} {-2,-4,-6,-8,……-2n}
Sn=n(1+2n-1)/2 = n^2
Sn'=n(-2-2n)/2 = -n(n+1) = -n^2-n
Sn+Sn' = n^2-n^2-n = -n
lim 1-2+3-4+...+(2n-1)-2n/ n -1
另外说一句,分母搞不清是n还是(n-1),一起讨论
lim [1-2+3-4+...+(2n-1)-2n/n] -1 = lim(-n/n)-1 = -2
lim 1-2+3-4+...+(2n-1)-2n/(n-1) = lim[-n/(n-1)] = -1