Using the Weierstrass M-test to show that $x^n$ converges uniformly on$ [-1/2,1/2]$ I need to use the Weierstrass M-test to show that $x^n$ converges uniformly on $[-1/2,1/2]$. Evidently one needs a sequence that converges and is strictly greater than $x^n$ here; What could one use as this sequence?

We have $|x^n|\leqslant\left(\frac12\right)^n$ and $$\sum_{n=1}^\infty \left(\frac12\right)^n=1, $$ and so we conclude.