Question

help with convergence..

Answer 1

\[\sum_{n=1}^{∞}(-1)^nn^{-1}f(n^{-1})\] where f: [0, 1] --> [0, 1] is a continuous increasing function with f(0) = 1/2

How can I show that this series i absolutely converges, conditional converges or divergent?

Answer 2

I would say it converges. I just tried with n ultralarge and got the term ultrasmall. But it's probably not enough... sry i can't help you further.

Answer 3

@ganeshie8

Answer 4

@Nurali

Answer 5

@Compassionate

Answer 6

@master43