$a_1=2,a_{n+1}=\frac{2^{n+1}a_n}{(n+\frac{1}{2})a_n+2^n}(n\in\mathbb{Z}_+)$ (a) Encontrar $a_n$ . (b) Sea $b_n=\frac{n^3+2n^2+2n+2}{n(n+1)(n^2+1)a_n}$ . Encontrar $S_n=\sum_{i=1}^nb_i$ .