# 5. Use appropriate tests to determine the convergence or divergence of the above series \text { (a) } \sum_{n=1}^{\infty} \frac{n^{2}+2 n+3}{4 n^{5}+n^{2}+3} \text { (b) } \sum^{\infty} \frac{\sqrt{n+c}}{\sqrt{n^{3}}+1} \text {

where } c>3 \text { is a constant } \text { (c) } \sum_{n=1}^{\infty} \frac{n^{2}+3 n+1}{3 n^{2}+4 n-1} \text { (d) } \sum_{n=1}^{\infty} \frac{4+2 \sin (n)}{3 n^{c}+4} \text { where } c>1 \text { is a constant } \text { (e) } \sum^{\infty} \frac{4+(-1)^{n}}{3 n^{c}+4} \text { where } 01 \text { is a constant } \text { (h) } \sum_{n=1}^{\infty} \frac{(-1)^{n} n^{2}}{3^{n}+2} \text { (i) } \sum_{n=1}^{\infty} \frac{c^{n}}{n^{4}+3} \text { where } c>1 \text { is a constant } \text { (j) } \sum_{n=1}^{\infty} \frac{n^{2}+2}{(-1)^{n} \cdot n !} (k) \sum_{n=1}^{\infty} \frac{n !}{n^{2}} \text { (1) } \sum_{n=1}^{\infty}\left(-\frac{1}{3}+\frac{1}{n}\right)^{n} \text { (m) } \sum_{n=1}^{\infty}\left(c+\frac{1}{n}\right)^{n} \text { where } c>1 \text { is a constant }