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March 31st, 2016, 07:46 AM  #1 
Senior Member Joined: Feb 2014 Posts: 114 Thanks: 1  Geometric progression
Hello, I need Geometric progression formula for this (attached) Thanks Last edited by skipjack; March 31st, 2016 at 07:52 AM. 
March 31st, 2016, 07:52 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
$2^{k+1}  1$

April 2nd, 2016, 06:28 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
You should know, if you are expected to be able to do a problem like this, that the general finite geometric sum (not "progression" that would be just the sequence 1, 2, 4, ...), $\displaystyle \sum_{i= 0}^N ar^n$, is equal to $\displaystyle \frac{a(1 r^{N+ 1}}{1 r}$. In your example, a= 1, r= 2, and N= k so the sum is $\displaystyle \frac{1 2^{k+1}}{1 2}= 2^{k+1} 1$ as skipjack said.


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