Determine the convergence, both pointwise and uniform, on [0,1] for the series

hint: look at the partial sums!

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- Mar 23rd 2011, 05:22 PMwopashuiDetermine the convergence, both pointwise and uniform
Determine the convergence, both pointwise and uniform, on [0,1] for the series

hint: look at the partial sums! - Mar 23rd 2011, 07:24 PMTheEmptySet
- Mar 23rd 2011, 08:57 PMAlso sprach Zarathustra
Perhaps a hint...:

Your series is telescopic. - Mar 24th 2011, 07:31 PMwopashui
- Mar 25th 2011, 08:11 AMTheEmptySet
- Mar 25th 2011, 08:33 AMPlato
- Mar 25th 2011, 07:30 PMwopashui
- Mar 25th 2011, 07:32 PMwopashui
- Mar 25th 2011, 08:01 PMTheEmptySet
That is exactly the point!

If you let you get the series

so the series converges pointwise to zero there

Now by the geometric series when the series converges to

so this sum converges to the function

Can a series of uniformly continuous functions converge to a discontinuous function? - Mar 25th 2011, 09:21 PMwopashui
- Mar 25th 2011, 10:39 PMTheEmptySet