Solve for the sum of the series: S=∑n=1∞1n(n+1)(n+2)S = \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)}S=∑n=1∞n(n+1)(n+2)1.
12\frac{1}{2}21
14\frac{1}{4}41
111
18\frac{1}{8}81