# Thread: does this series converge?

1. ## does this series converge?

$\sum {\frac {2+sin^3(n+1)} {2^n + n^2} }$

Can someone show me this plz?

2. Originally Posted by Cato
$\sum {\frac {2+sin^3(n+1)} {2^n + n^2} }$

Can someone show me this plz?
note that $\Bigg| \frac {2 + \sin^3 (n + 1)}{2^n + n^2} \Bigg| \le \Bigg| \frac {2 + 1}{2^n + n^2} \Bigg| = \Bigg| \frac 3{2^n + n^2} \Bigg|$

now what can you say?

3. $\Bigg| \frac 3{2^n + n^2} \Bigg|$ < $\Bigg| \frac 3{n^2} \Bigg|$ which we know converges so the whole thing converges, right?

4. Originally Posted by Cato
$\Bigg| \frac 3{2^n + n^2} \Bigg|$ < $\Bigg| \frac 3{n^2} \Bigg|$ which we know converges so the whole thing converges, right?
yes, it converges absolutely by the comparison test. and absolute convergence implies convergence