Question

Weierstrass' M-test

Answer 1

How can I show that the series
\[\sum_{n=1}^{∞}n^{-p}e^{inx}\]
is uniformt convergent with the Weierstrass M test?

Answer 2

look at this, it may help http://www.unco.edu/nhs/mathsci/facstaff/Roberson/Docs/MATH%20632/Weierstrass%20M-Test.pdf

Answer 3

I know the series is uniform convergence when p>1. But can I prove it this way?
\[\left| n^{-p}e^{inx}\right|≤\frac{ 1 }{ n^p}\]
???

Answer 4

@.Sam. Can you help me?

Answer 5

yes of course ... Weirstrass M test is strong test.

Answer 6

but you need to show that 1/n^p converges uniformly. for that you can use Cauchy test.