# Difficult sums

Hello. I'm interested in computing the sum $$\large \displaystyle \sum_{n=1}^\infty 2^{-2^n}$$. Does anyone have any exact methods?

Note by Sal Gard
2 years, 4 months ago

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Your number is equal to the Fredholm number minus $$2^{-2^0} = \dfrac12$$. Since Fredholm number has been proven to be a transcendental numbers, then there is no way of finding closed form for this number.

- 2 years, 4 months ago