Excel in math, science, and engineering

New user? Sign up

Existing user? Sign in

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 1 year, 2 months ago

Sort by:

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. – Pi Han Goh · 1 year, 2 months ago

Log in to reply

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestYour 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. – Pi Han Goh · 1 year, 2 months ago

Log in to reply