# Help with calculating geometric sequence

• Jun 28th 2013, 01:29 AM
Stormey
Help with calculating geometric sequence
Hi,
I hope it is the right place to post it...

I need help with the following sequence:

$\displaystyle \sum_{i=0}^{j}2^{2^i}=N$

(it's 2 to the power of 2 to the power of i)

I need to find i as a function of N.
meaning how further away in the sequence do i need to go, in order to get N.

any help would greatly appreciated.
• Jun 28th 2013, 02:53 AM
chiro
Re: Help with calculating geometric sequence
Hey Stormey.

Did you mean as a function of j?

I don't know of a closed form solution but you should look into techniques like Euler-Mclaurin series and their relationship to integrals.
• Jun 28th 2013, 04:18 AM
Stormey
Re: Help with calculating geometric sequence
Hi chiro.
yes, as a function of j, sorry.
the truth is that it is actually a question from data starctures in computer science, so I almost sure the solution suppose to be accomplished with discrete math.
(using some manipulation to compute the sum of a more simple sequence, to which the sum is known or easy to calculate, and then calculating the sum of the original sequence,
I also tried to think about some change of variable [index in this case], that will help simplify this problem)
• Jun 28th 2013, 04:41 PM
chiro
Re: Help with calculating geometric sequence
You might want to consider a bit-wise representation (i.e. binary) and how that relates to N.