Evaluate the partial sum S2S_2S2 for the series ∑n=1∞1n(n+1)\sum_{n=1}^{\infty} \frac{1}{n(n+1)}∑n=1∞n(n+1)1.
12\frac{1}{2}21
23\frac{2}{3}32
34\frac{3}{4}43
111