Valid application of Weierstrass Test?

[end3r7]

It would seem so

Homework Statement

If
$$\sum\limits_{n = 1}^{\inf } {|{f(n,x)}|}$$ is uniformly convergent on [a,b], then is $$\sum\limits_{n = 1}^{\inf } {{f(n,x)}}$$ 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

 

[quasar987]

I don't follow your argument.

Just because a series converge uniformly does not mean it satisfy Weierstrass' M test

 

[end3r7]

Well, forget the Weierstrass test then...
If one is uniformly Cauchy, wouldn't that make the toher essentially uniformly Cauchy as well?

 

[quasar987]

This sounds right! (triangle inequality)

 

[Xiola168]

How does uniformly Cauchy apply to absolute uniform convergence