Determine whether the sequence converges or diverges. If it converges, find what it converges to. \text { 1.) a.) } a_{n}=\frac{3+5 n^{2}}{n+n^{2}} \text { b.) } a_{n}=\frac{(-1)^{n-1} n}{n^{2}+1} \text {

c.) } a_{n}=\sqrt{\frac{n+1}{9 n+1}} \text { d.) } a_{n}=\frac{\sin 2 n}{1+\sqrt{n}}