Question: Test given series for convergence or divergence. If the series converges and it is possible to find the sum, then do so

(a) \(\sum\limits_{n=1}^{\infty }{\frac{1}{n\left( n+1 \right)}}\)

(b) \(\sum\limits_{n=1}^{\infty }{\frac{\ln n}{{{n}^{2}}}}\)

(c) \(\sum\limits_{n=1}^{\infty }{\frac{2{{n}^{2}}+3n}{\sqrt{5+{{n}^{5}}}}}\)

(d) \(\sum\limits_{n=1}^{\infty }{\frac{{{\left( n! \right)}^{2}}}{\left( 3n! \right)}}\)