Let a (0,1). Show that the functional series

where

is uniformly convergent with the limit function

I have absolutely no clue where to go from here.

Any help???

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- Nov 28th 2010, 04:20 PMgarunasFunctional Series and Uniform Convergence Question
Let a (0,1). Show that the functional series

where

is uniformly convergent with the limit function

I have absolutely no clue where to go from here.

Any help??? - Nov 28th 2010, 07:09 PMDrexel28
Merely note that for , but since converges, it follows by the Weierstrass M-test that converges uniformly on . To prove what it sums to merely note that