Uniform convergence of series: $\sum_{n=1}^{\infty}{2^n\sin\left(\frac{x}{3^n}\right)}$ Task: we should find area of x>=0, that the series is Uniform convergence on this area
$$\sum_{n=1}^{\infty}{2^n\sin\left(\frac{x}{3^n}\right)}$$
There are some ways to proof "Uniform convergence of sum". 
I tried to use Dirichlet and Abel's ways to solve, but they are not suited on this case.
However, I checked answers and got: it is not converges uniformly

Hint:
If $t>0$ then $\sin t<t$.
