# Math Help - Weierstrass M-test

1. ## Weierstrass M-test

So thanks to tph we know that $\sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k}$ converges on $(-\sqrt{\frac{3}{2}}, \sqrt{\frac{3}{2}})$.

To use the Weierstrass M-test, how do we find a bound for that sum.

Thanks

2. Originally Posted by tbyou87
So thanks to tph we know that $\sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k}$ converges on $(-\sqrt{\frac{3}{2}}, \sqrt{\frac{3}{2}})$.

To use the Weierstrass M-test, how do we find a bound for that sum.

Thanks
What are you trying to show? We can show that if $0 where $R=\sqrt{3/2}$ then $\sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k}$ converges uniformly on $[-r,r]$ by choosing $M_k = \frac{k2^k}{3^k}r^{2k}$.