Determine Whether the Series Is Convergent or Divergent by Expressing $S _ { n }$

Determine whether the series is convergent or divergent by expressing $S _ { n }$ as a telescoping sum. If it is convergent, find its sum. $\sum _ { n = 1 } ^ { \infty } \frac { 14 } { n ^ { 2 } + 2 n }$ .

A) $\frac { 1 } { 14 }$
B) $\frac { 21 } { 2 }$
C) $\frac { 2 } { 21 }$
D) $2$
E) diverges

Correct Answer:

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