It would seem so(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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

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# Valid application of Weierstrass Test?

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