lim(x^n-1)/(x-1)(x趋向于1n为正整数)的极限
问题描述：
lim(x^n-1)/(x-1)(x趋向于1n为正整数)的极限
答
(x^n-1)'/(x-1)'=nx^(n-1)/1=nx^(n-1)
x->1，x^(n-1)->1
lim(x^n-1)/(x-1)=n
x->1
答
lim(x^n-1)/(x-1)=limx^(n-1)+x^(n-2)+...+1
故x趋向于1时,其极限为n