if we have

sum{n=0/to infinit} f_n (x)

such that n in N and x in [-1.1]

f_n =x/(1+x^2)^n

r this series confergence?is it uniform convergence?

:confused:

Printable View

- May 24th 2006, 01:19 AMsweetuniform convergence
if we have

sum{n=0/to infinit} f_n (x)

such that n in N and x in [-1.1]

f_n =x/(1+x^2)^n

r this series confergence?is it uniform convergence?

:confused: - May 24th 2006, 01:40 PMThePerfectHackerQuote:

Originally Posted by**sweet**

Thus, and apply the ratio test,

This gives,

It converges*absolutely*when,

Thus,

Thus, .

It diverges when,

thus,

WHich is impossible.

It is inconclusive when, ,

Thus, .

But we can this that this series is convergent abolsutely thus, this is absolutely convergenet everywhere. - May 24th 2006, 02:44 PMsweet
ok now we know it's convergence but what about uniform convergence