Determine whether the sequence convergent or divergent. $\sum _ { n = 1 } ^ { \infty } \frac { 5 } { n ^ { 2 } + 5 }$
A) converges
B) diverges

Question

Quizplus · Accepted Answer

To determine if the series converges or diverges, we can use the p-series test with p=2. 
$$\sum _ { n = 1 } ^ { \infty } \frac { 5 } { n ^ { 2 } + 5 } \leq \sum _ { n = 1 } ^ { \infty } \frac { 5 } { n ^ { 2 } } = \frac{5\pi^2}{6}$$
Since the sum converges (p-series test), the given series also converges.

Determine Whether the Sequence Convergent or Divergent ∑n=1∞5n2+5\sum _ { n = 1 } ^ { \infty } \frac { 5 } { n ^ { 2 } + 5 }∑n=1∞​n2+55​

Determine Whether the Sequence Convergent or Divergent $\sum _ { n = 1 } ^ { \infty } \frac { 5 } { n ^ { 2 } + 5 }$