局部 与 整体 修正 逐渐逼近

 

n!<= [(n+1)/2]^n
(n+1)!<= [(n+2)/2]^(n+1)

(n+1)!<[(n+1)/2]^n*(n+1)
= [(n+2)/2]^(n+1) *(n+1) *[2/(n+2)]*(n+1/n+2)^n
= A*2*(n+1/n+2)^(n+1)
= A*2/[(1+1/n+1)^(n+1)]
<A

2!*4!*...*(2n)!>[(n+1)!]^n
2!*4!*...*(2n)!*(2n+2)! > [(n+2)!]^(n+1)

[(n+2)!]^(n+1)=[(n+1)!]^n*[(n+2)!]*(n+2)^n
(2n+2)! > [(n+2)!]*(n+2)^n
(n+3)*...*(2n+2)>(n+2)^n