Which of these series has a partial sum SnS_nSn defined by Sn=2nn+2S_n = \frac{2n}{n+2}Sn=n+22n?
∑n=1∞4n(n+2)\sum_{n=1}^{\infty} \frac{4}{n(n+2)}∑n=1∞n(n+2)4
∑n=1∞2n(n+1)\sum_{n=1}^{\infty} \frac{2}{n(n+1)}∑n=1∞n(n+1)2
∑n=1∞12n\sum_{n=1}^{\infty} \frac{1}{2^n}∑n=1∞2n1
∑n=1∞nn2+1\sum_{n=1}^{\infty} \frac{n}{n^2+1}∑n=1∞n2+1n