A First Course in Complex Analysis · Problem 7.5.18

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · series-convergence-divergence

Problem

(a) Show that

\displaystyle\sum_{k\geq 1} \frac{k}{k^2+1}

diverges. (b) Show that

\displaystyle\sum_{k\geq 1} \frac{k}{k^3+1}

converges.