Question

lim

x→1

x+x2+…+xn-n

x-1

=______．

Answer 1

设A=

x+x2+…+xn-n

x-1

=

(x-1)+(x2-1)+…+(xn-1)

x-1

=1+（x+1）+（x²+x+1）+…+（x^n-1+x^n-2+…+1）
所以

lim

n→1

A=

lim

n→1

[1+（x+1）+（x²+x+1）+…+（x^n-1+x^n-2+…+1）]=1+2+3+…+n=

n(n+1)

2

故答案为

n(n+1)

2

．