Prove or give a counter example $ \sum_{n=1}^{\infty } a_{2n} \ and \sum_{n=1}^{\infty } a_{2n-1} $ converge than $ \sum_{n=1}^{\infty } a_{n} $
Prove that if $\sum_{n=1}^\infty a_{2n}$ and $\sum_{n=1}^\infty a_{2n-1}$ converge then $\sum_{n=1}^\infty a_n$ converges.