Prove: If the terms of a convergent series $\sum a_{n}$ have the same sign for $n \geq k$, then $\sum a_{n}$ converges absolutely.
It seems to make sense when reading it, but I'm not sure I understand where to start my proof. Any help would be appreciated.
absolut convergence is with |..|. If you know that after an $n_0$ they all have the same sign you can take out of the sum the first $n_0 -1$ terms. They are finite number so doesn't care becouse they are finish. If the terms after $n_0$ are positive at that point you are looking already for absolut convergence. If the terms after $n_0$ are negative you just have to put a - in front of the sum and you will be looking for absolut convergence.