Question

lim 1-2+3-4+...+(2n-1)-2n/ n -1=多少

如题

Answer 1

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

Answer 2

=-1
1-2=-1
3-4=-1
。。。

lim-1*（n-1）/n-1