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end3r7

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## Homework Statement

If

[tex]

\sum\limits_{n = 1}^{\inf } {|{f(n,x)}|}

[/tex] is uniformly convergent on [a,b], then is [tex]

\sum\limits_{n = 1}^{\inf } {{f(n,x)}}

[/tex] uniformly convergent.

## Homework Equations

## The Attempt at a Solution

I said yes. And just applied the Weierstrass Test with |f(n,x)| <= |f(n,x)| (a basic comparison test)

Should still be valid right? Since the absolutely value is Uniformly Cauchy