Question

求lim[(2n-1）/（2n+1)]^n,n趋于无穷

Answer 1

这是1^∞型极限,利用重要极限lim(x→∞) [1+(1/x)]^x=e
lim(x→∞) [(2n-1)/(2n+1)]^n
=lim(x→∞) [1-2/(2n-1)]^n
=lim(x→∞) [1-2/(2n-1)]^{[-(2n-1)/2]*[-2n/(2n-1)]}
=e^ {lim(x→∞) [-2n/(2n-1)]}
=e^(-1)
=1/e