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?
2026-04-17 21:27:37.1776461257
Using the Weierstrass M-test to show that $x^n$ converges uniformly on$ [-1/2,1/2]$
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We have $|x^n|\leqslant\left(\frac12\right)^n$ and $$\sum_{n=1}^\infty \left(\frac12\right)^n=1, $$ and so we conclude.