fuss:mathematics:calculus:series:convergence:alternating [Wizardry and Steamworks]

Consider the alternating series:

$\sum_{k=0}^{\infty}(-1)^{k}a_{k}$

where $a_{k} > 0, \forall k \ge 0$

if $a_{k+1} < a_{k}, \forall k \text { and } \lim_{a_{k}}=0$ then the series converges.