April 19th, 2017, 12:24 PM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 154 Thanks: 21  Does series converge?
$\displaystyle \sum_{i=1}^{\infty} \frac{\sin n^3 x}{n^2}$

April 19th, 2017, 12:59 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,610 Thanks: 1292 
note ... $\bigg\dfrac{\sin(n^3 x)}{n^2}\bigg \le \dfrac{1}{n^2}$ 

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conerge, converge, serie, series 
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