# Sum of inverse of Fermat's numbers

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?

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