Derivative of a series - GRE Mathematics Subject Test

Submit your math problems to me at [e-mail] and I'll attempt a solution as I see it for the first time.
Follow me on Twitter: / mathoutloud40
Follow me on Mastodon: mathstodon.xyz...

[@devotion7890]

If I'm not mistaken, you can also find a closed expression for f(x) in this way, namely by integrating f'(x), i.e. in this case integrating the geometric series. This then gives the function -log(1-x) for f(x)

[@mathoutloud]

Absolutely! And I should have recognized the original series as something related to the logarithm anyway.