Question

Need help with Fourier series.

Answer 1

Consider, for all p> 0, the number of trigonometric series
\[\sum_{n=1}^{∞}n^{-p}e^{inx}\]
How can I show that for p> 1, that the Fourier series is a continuous 2π-periodic function.

Answer 2

I think I maybe have to use eulers formel.

Answer 3

Like this:
\[n^{-p}\cos(nx)*i*\sin(x)\]