Limit [(x∧n-1)/(x-1)]这道题怎么做呀?
问题描述：
Limit [(x∧n-1)/(x-1)]这道题怎么做呀?
答
Limit [(x∧n-1)/(x-1)]
应当加上x->1吧
Limit [(x∧n-1)/(x-1)]
x->1
=Limit [(x-1)(x^(n-1)+x^(n-2)+……＋x+1)/(x-1)]
x->1
=(n-1)*1+1
=n
关键点在于分解因式：
x∧n-1=(x-1)(x^(n-1)+x^(n-2)+……＋x+1)