I should be able to figure this out, but it has me a bit confused conceptually. I'm really just not sure how to approach it in a rigorous fashion. Any help?
If $a_0, a_1, a_2, . . .$ is a decreasing sequence of positive numbers, then the alternating series $a_0−a_1+a_2−a_3+a_4−a_5+· · ·$ converges to some value $L$. Prove that $0 < L < a_0$.