Xn=[(n-1)/(n+1)]^n 求数列极限

Question

如题所述

Answer 1

lim
[(n-1)/(n+1)]^n
=lim
[(n+1-2)/(n+1)]^n
=lim
[1+(-2)/(n+1)]^n
=lim
[1+(-2)/(n+1)]^(n+1-1)
=lim
[1+(-2)/(n+1)]^(n+1)
*
[1+(-2)/(n+1)]^(-1)
=lim
[1+(-2)/(n+1)]^(n+1)
*
lim
[1+(-2)/(n+1)]^(-1)
=lim
[1+(-2)/(n+1)]^(n+1)
*
1
=lim
[1+(-2)/(n+1)]^[(n+1)/(-2)
*
(-2)]
=lim
{[1+(-2)/(n+1)]^[(n+1)/(-2)]}^(-2)
={lim
[1+(-2)/(n+1)]^[(n+1)/(-2)]}^(-2)
根据重要
极限：lim
(1+1/n)^n=e
=e^(-2)
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