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des
Jun 22, 2020

I wanted to know how to derive the series for ln(2)

Looking back at what I did. I think I made a lot of mistakes, but I don't know if I'm correct in saying that I am wrong. (Pls answer!) Thanks. [See attached file]

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Ian Fowler
Jun 23, 2020

I did pretty much the same thing. Integrating both 1/(1+x) and the infinite geometric series term by term. The bottom line is that there is convergence to ln(2) when x = 1 but someone else is going to have to weigh in as to how the radius of convergence -1<x<1 in the original sequence now somehow changes to -1<x<=1 for ln(x+1). Not much of a help for you but I agree with you that you have identified the key sticking point.