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

1. \(\sum\limits_{n=1}^{\infty }{\frac{1}{n\left( n+1 \right)}}\)
2. \(\sum\limits_{n=1}^{\infty }{\frac{\ln n}{{{n}^{2}}}}\)
3. \(\sum\limits_{n=1}^{\infty }{\frac{2{{n}^{2}}+3n}{\sqrt{5+{{n}^{5}}}}}\)
4. \(\sum\limits_{n=1}^{\infty }{\frac{{{\left( n! \right)}^{2}}}{\left( 3n! \right)}}\)

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