I came across the following series while solving my math problem:
$$ \sum_{x=1}^\infty \frac{1}{2^x - 1} $$
While it's easy to check the convergence of the series, finding the sum itself seems to be tricky.
How to find the value of this sum?
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2It is less than $2$, see here. It is called the Erdös-Borwein constant, which is around $1.6066$. – Dietrich Burde Sep 12 '24 at 12:09
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3This question is similar to: About the Erdős-Borwein Constant. If you believe it’s different, please edit the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem. See also this duplicate. – Dietrich Burde Sep 12 '24 at 12:12
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Thank you for a reference! The main difference is that I'm actually interested in derivation of the formula. However, I believe that given its name I will be able to find it on my own. – Dark_Furia Sep 12 '24 at 13:33