求极限lim(n→∞)(a^n+(-b)^n)/(a^n+1+(-b)^n+1)

题目

求极限lim(n→∞)(a^n+(-b)^n)/(a^n+1+(-b)^n+1)

答案

n→+∞时
[a^n+(-b)^n]/[a^(n+1)+(-b)^(n+1)]
={[1+(-b/a)^n]/[a-b(-b/a)^n]→1/a,|a|>|b|;
.{[(-a/b)^n+1]/[a(-a/b)^n-b]→-1/b,|a|