Question

E. Show that if $\sum_{n=1}^{\infty} |a_n| < \infty$, then $\sum_{n=1}^{\infty} a_n \cos nx$ converges uniformly on $\mathbb{R}$.

Name: E. Show that if ∑n=1^∞ |an| < ∞, then ∑n=1^∞ an cos nx converges uniformly on ℝ.
Uploaded: 2024-03-07T17:27:31-08:00
Duration: 4 min 37 s
Channel: Mengchun Cai
Description: E. Show that if ∑n=1^∞ |an| < ∞, then ∑n=1^∞ an cos nx converges uniformly on ℝ.

          E. Show that if $\sum_{n=1}^{\infty} |a_n| < \infty$, then $\sum_{n=1}^{\infty} a_n \cos nx$ converges uniformly on $\mathbb{R}$.

Added by Glenda V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Mengchun Cai

03/07/2024

Step 1

We are given that $\sum_{n=1}^{\infty} |a_n| < \infty$. We want to show that $\sum_{n=1}^{\infty} f_n(x)$ converges uniformly on $\mathbb{R}$. Show more…

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