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## Homework Statement

Prove that the function [tex] f(x) = \sum_{n=1}^{\infty} \frac{cos(n^2x)}{e^{nx^2}2^n} [/tex] is continuous on R.

## Homework Equations

## The Attempt at a Solution

I haven't learned about a series of functions converging to a function yet, but would it be sufficient to show that each function in the infinite sum is differentiable, so each function in the infinite sum is continuous, meaning that the sum of the functions must also be continuous?