- #1
end3r7
- 171
- 0
It would seem so
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.
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
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