Easy way vs hard way

[@actions-speak]

The sum is equal to the sum of x^(2n+1)/(2n+1) - x^(2n)/2n evaluated at x=1. This second sum is the integral with respect to x of 1/(1-x^2) - 1 - x/(1-x^2) evaluated at x = 1. This expression simplifies to log(1+x) - x evaluated at x = 1, log(2) - 1.

[@owlsmath]

nice one

[@reaperskyfall6691]

Method was good sir and please pray for my exams in December 20 then over and can happily go to home.😊

[@owlsmath]

thanks Good luck Skyfall! Wish you good luck on your exams! 😀👍👍👍

[@MikeMagTech]

The easy and quick way is typically more practical, but I often find the hard way to be more fun and educational...yes, the two really do go hand in hand even though our society likes to give people the impression that learning is a punishment. I know I am getting a bit political, but I think that is a terrible attitude that leads to moral decay.

[@owlsmath]

Hey Mike. thanks and good points. I've been kind of battling with this idea and its a tricky balance of showing the straightforward quick ways vs the "alternative methods". 👍