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)
根据重要的极限：lim (1+1/n)^n=e
=e^(-2)
有不懂欢迎追问
