求limx+x^2+.+x^n-n/x-1 (x趋于1)

原式=
Lim[∑(x^k)-n]／(x-1)(k=1到 n的自然数)
x→1
=Lim[(x-1)／(x-1)＋(x^2-1)／(x-1)＋...＋(x^n-1)／(x-1)]
x→1
=Lim{1＋(x+1)＋...＋[x^(n-1)+x^(n-2)+--+x+1)]}
x→1
=1+2+...+n
=n(n+1)／2