Find the sum of ∑n=1∞2n+1n2(n+1)2\sum_{n=1}^{\infty} \frac{2n+1}{n^2(n+1)^2}∑n=1∞n2(n+1)22n+1.
111
000
12\frac{1}{2}21
14\frac{1}{4}41