# Checking the convergence of two series

1.$\sum_{n=2}^{\infty}\left(\frac{1}{n^{1/2}}\right)\ln\left(\frac{n+1}{n-1}\right)$...For this series I just have one logic that it is product of two divergent series i.e.first is $\sum (1/n^{1/2})$ and the remaining one..so I think the original series should diverge..but I doubt on this..