Evaluate the series ∑n=1∞1n(n+3)\sum_{n=1}^{\infty} \frac{1}{n(n+3)}∑n=1∞n(n+3)1 using partial fractions decomposition.
1118\frac{11}{18}1811
13\frac{1}{3}31
19\frac{1}{9}91
518\frac{5}{18}185