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lim(x→1)(x^n-1)/(x-1),=（x-1+1)^n=(x-1)^n+n(x-1)^(n-1)+......+n(x-1)^1+1
题目详情
lim(x→1)(x^n-1)/(x-1),
=（x-1+1)^n
=(x-1)^n+n(x-1)^(n-1)+......+n(x-1)^1+1
=（x-1+1)^n
=(x-1)^n+n(x-1)^(n-1)+......+n(x-1)^1+1
▼优质解答
答案和解析
x^n=（x-1+1)^n
=(x-1)^n+n(x-1)^(n-1)+.+n(x-1)^1+1
则(x^n-1)/(x-1)=(x-1)^(n-1)+n(x-1)^(n-2)+.n(n-1)(x-1)/2+n
则lim(x->1):(x^n-1)/(x-1) =n
=(x-1)^n+n(x-1)^(n-1)+.+n(x-1)^1+1
则(x^n-1)/(x-1)=(x-1)^(n-1)+n(x-1)^(n-2)+.n(n-1)(x-1)/2+n
则lim(x->1):(x^n-1)/(x-1) =n
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