Solving n factorial if it converges or diverages

[Nikki_gurl03]

I have
Summation of n=1 to infinity of n factorial/ln(n+1)

I started the ratio test but got suck on the lim of ((n+1)ln(n+1))/(ln(n+2))[/list]

 

[skeeter]

term for term, \(\displaystyle \L \frac{n!}{\ln(n+1)} > \frac{n}{\ln(n+1)}\)

show that the nth term of \(\displaystyle \L \frac{n}{\ln(n+1)}\) does not approach 0 (and therefore, diverges).