I got a nice "Alternative Method" from the comments

[@reaperskyfall6691]

Understand very well

[@owlsmath]

Hey Skyfall. Good to hear it!

[@owlsmath]

Convergence for geometric series is |x| < 1

[@MikeMagTech]

I really enjoyed that. It was obvious you meant |x| < 1 so no worries.

[@owlsmath]

@@MikeMagTech great :) Yeah i am so used to showing that i think i got a little lazy

[@ethanbartiromo2888]

You sound exactly like my friend Alex

[@owlsmath]

Interesting. I can tell you that I’m not him but I am waiting for the day that someone can either recognize my voice or hand from the videos 😂

[@doronezri1043]

Beautiful👏👏👏 How about using Feynman's with x^a/(1+x) and then employing the geometric series (as you did)? This way you can "bypass" the IBP🍻

[@holyshit922]

Whats wrong in IBP and why you want to avoid it with all costs

[@owlsmath]

nice Thanks! Does that work out ok that way? I tried it briefly but what I came to was something similar to what I had in the video that led to the IBP :)

[@doronezri1043]

@@holyshit922 Not "all costs", just a little simpler😀

[@holyshit922]

@@doronezri1043 In fact your proposition is more complicated so with all costs are right words
Moreover you didn't explain what's wrong with IBP

[@actions-speak]

Very nice!

[@owlsmath]

Thanks!

[@holyshit922]

At the end you could split this sum into even ad odd terms to use solution of Basel problem

[@owlsmath]

yep I think thats how I did it in the video i mentioned where I derive it but I don't remember it for certain

[@holyshit922]

@@owlsmath You can derive solution of Basel problem by comparing product expansion and series expansion of sin(x)/x

[@tfg601]

redefine as x:= x+1 and then use another substitution u = ln(x - 1)

[@owlsmath]

and then what happens next?

[@vlad-ji1lz]

Shouldnt be |x|

[@owlsmath]

Yeah. Sorry bad mistake 😮