What is the sum of inverse of all Fermat's numbers? I know the series is convergent using comparison by geometric series with common ratio 1/2 and first term 1/2 but I don't know how to find the sum?

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    $\begingroup$ I'm almost 100% sure we are not able to relate it to any known constants with our current knowleadge. $\endgroup$ – Jorge Fernández Hidalgo Jul 19 '15 at 7:29
  • $\begingroup$ See OEIS A$051158$. $\endgroup$ – Lucian Jul 19 '15 at 10:35

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