Prove that, if $a_k \geq 0$ for large $k$, and that $$\sum_{k=1}^\infty \frac{a_k}{k}$$ converges. Prove that $$\lim_{j \rightarrow \infty} \sum_{k=1}^\infty \frac{a_k}{j+k} = 0$$
I believe I cant write $$\sum_{k=1}^\infty \frac{a_k}{j+k} \leq \sum_{k=1}^\infty \frac{a_k}{k}.$$ However, taking limit does not give me the answer.