Answer to Question #251233 in Real Analysis for Sourav Mondal

Question

Use Mn test to prove that the series n ²x ² converges uniformly in [-1/4,1/3] .

Answer 1

Since

$|n^{-2}x^2|<n^{-2}$ in [-1/4, 1/3]

and

$\sum n^{-2}$ converges

then

$\sum n^{-2}x^2$ converges in [-1/4, 1/3]