Determine whether the sequence convergent or divergent.
$$\sum _ { n = 1 } ^ { \infty } \frac { 3 } { n ^ { 2 } + 3 }$$
A) converges
B) diverges

Question

Quizplus · Accepted Answer

We will use the comparison test. 
Since $n^2+3$ is always greater than $n^2$, we have 
$$\frac{3}{n^2+3} < \frac{3}{n^2}$$
Since $\sum_{n=1}^\infty \frac{3}{n^2}$ converges (it is a $p$-series with $p=2>1$), by the comparison test, $\sum_{n=1}^\infty \frac{3}{n^2+3}$ converges as well.

Determine Whether the Sequence Convergent or Divergent ∑n=1∞3n2+3\sum _ { n = 1 } ^ { \infty } \frac { 3 } { n ^ { 2 } + 3 }n=1∑∞​n2+33​

Determine Whether the Sequence Convergent or Divergent $\sum _ { n = 1 } ^ { \infty } \frac { 3 } { n ^ { 2 } + 3 }$