Question

Show that the series Σ1/(1+xn^2) converges uniformly on [a,∞) for any a>0 but does not converge uniformly on (0,∞).

Answer 1

\[\sum 1+(1+xn^2)\] is the series?

Answer 2

yes

Answer 3

But that doesn't converge for any value of x because \(\lim_{n \to \infty} (2+xn^2)=\infty\) for all x.

Answer 4

Um, she said yes, but I think that's not the series. The series she typed in her first post is
\[\sum \frac{1}{1+xn^2}\]

Answer 5

That's because she edited her post.

Answer 6

lols