{[(n+1)^(n+1)]/(n+1)!}*[n!/(n^n)]=?请高手赐教,最好写出步骤,

问题描述:

{[(n+1)^(n+1)]/(n+1)!}*[n!/(n^n)]=?请高手赐教,最好写出步骤,

{[(n+1)^(n+1)]/(n+1)!}*[n!/(n^n)]
=n!/(n+1)! * [(n+1)^(n+1)]/(n^n)
=1/(n+1) * [(n+1)^(n+1)]/(n^n)
= (n+1)/(n^n)
= 1/n + 1/(n^n)

[(n+1)^(n+1)/(n+1)!][n!/n^n]
={[(n+1)/n]^n}(n+1)[n!/(n+1)!]
={[(n+1)/n]^n}(n+1)/(n+1)
=[(n+1)/n]^n