Determine the sum of the series ∑n=1∞1n(n+1)(n+2)\sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)}∑n=1∞n(n+1)(n+2)1.
12\frac{1}{2}21
14\frac{1}{4}41
18\frac{1}{8}81
16\frac{1}{6}61