Suppose that $\displaystyle a_k \to \infty$ as $\displaystyle k \to \infty$. Prove that $\displaystyle \displaystyle\sum_{k=1}^{\infty} a_k$ converges if and only if the series $\displaystyle \displaystyle\sum_{k=1}^{\infty} (a_{2k} + a_{2k+1})$ converges.