Proving continuity of the limit function of $\sum_{k=1}^{\infty} \frac{\sin(k^3 x)}{2^k}$. Consider the series $\sum_{k=1}^{\infty} \frac{\sin(k^3 x)}{2^k}$.
Prove that the limit function is continuous. 
I'm confused on what a limit function is...?

Hint:
$0\le \left|\dfrac{\sin(k^3x)}{2^k}\right|\le \dfrac 1{2^k}.$
