已知函数f(x)=(1+ln(x+1))/x,(x>0),求证:(1+1·2)(1+2·3)(1+3·4)···(1+n(n+1))>e^(2n-3)
问题描述:
已知函数f(x)=(1+ln(x+1))/x,(x>0),求证:(1+1·2)(1+2·3)(1+3·4)···(1+n(n+1))>e^(2n-3)
答
(1+1·2)(1+2·3)(1+3·4)···(1+n(n+1))>e^(2n-3)不等式两边同时取以e为底的对数得ln((1+1·2)(1+2·3)(1+3·4)···(1+n(n+1)))>2n-3即ln(1+1·2)+ln(1+2·3)+……+ln(1+n(n+1))>2n-3可以利...