Determine Whether the Given Series Is Convergent or Divergent $\sum _ { n = 1 } ^ { \infty } \frac { 2 n ^ { 2 } + 1 } { 5 n ^ { 3 } - n + 4 }$

Determine whether the given series is convergent or divergent. Indicate the test you use and show any necessary computation.(a) $\sum _ { n = 1 } ^ { \infty } \frac { 2 n ^ { 2 } + 1 } { 5 n ^ { 3 } - n + 4 }$ (e) $\sum _ { n = 1 } ^ { \infty } \tan ^ { - 1 } n$ (i) $\sum _ { n = 1 } ^ { \infty } \frac { 4 ^ { n } } { 2 ^ { n } + 3 ^ { n } }$ (b) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 1 + \sin n } { n } \right) ^ { 2 }$ (f) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n \sqrt { 1 + \ln n } }$ (j) $\sum _ { n = 1 } ^ { \infty } \ln \left( 1 + \frac { 1 } { n } \right)$ (c) $\sum _ { n = 1 } ^ { \infty } n \cdot \sin \left( \frac { 1 } { n } \right)$ (g) $\sum _ { n = 1 } ^ { \infty } \frac { \ln n } { ( n + 1 ) ^ { 3 } }$ (k) $\sum _ { n = 1 } ^ { \infty } n \cdot e ^ { - n ^ { 2 } }$ (d) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 } { n \sqrt { n } } + \frac { 3 } { n ^ { 3 } } \right)$ (h) $\sum _ { n = 1 } ^ { \infty } \frac { \ln n } { n }$

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(a) Diverges
(b) Converges
(c)...

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