I think understand that when I have a conditionally convergent series, it consists of series of positive and negative values which are divergent and thus one can find such permutation of indices $\phi : \mathbb{N}\rightarrow\mathbb{N}$ so the rearranged series sums up to an arbitrary value, diverges or oscillates.
This is how I understand what Riemann's rearrangement theorem says, but how do I use it practically? For example, when I have the conditionally convergent series:
$\sum_{n=1}^{\infty}\frac{(-1)^n}{\sqrt{n}}$
and I want to rearrange it to be divergent or to sum up to certain value M? How do I define such bijections $\phi$ ?
I appreciate all help.