求lim[(2n-1)/(2n+1)]^n,n趋于无穷

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求lim[(2n-1)/(2n+1)]^n,n趋于无穷求lim[(2n-1)/(2n+1)]^n,n趋于无穷求lim[(2n-1)/(2n+1)]^n,n趋于无穷这是1^∞型极限,利用重要极限lim(

求lim[(2n-1)/(2n+1)]^n,n趋于无穷
求lim[(2n-1)/(2n+1)]^n,n趋于无穷

求lim[(2n-1)/(2n+1)]^n,n趋于无穷
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

lim[(2n-1)/(2n+1)]^n
=lim[1-2/(2n+1)]^n
=1