I am looking at the following problem, and can intuitively see that it is true, but i am having trouble proving it:
Assume that the function $f$ is $2π$-periodic and has the Fourier series
$$f(x)=a_0 + \sum_{n=1}^\infty (a_n \cos(nx) + b_n \sin(nx))$$
Let $k \in N$. Show that the function $g(x) = f(kx)$ is $2π$-periodic, too.
All help is welcome!
No need for Fourier series here ;) $$g(x+2\pi n) = f(k(x+2\pi n)) = f(kx + 2\pi nk) = f(kx) = g(x)$$