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 April 29th, 2014, 12:59 PM #1 Senior Member   Joined: Nov 2013 Posts: 434 Thanks: 8 sequence The sum of the first n terms of the sequence $1,~(1+2),~(1+2+2^2),~\dots ~(1+2+2^2+\dots+2^{n-1})$
 April 29th, 2014, 01:42 PM #2 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 $\displaystyle \sum_{j=0}^{n-1}\sum_{i=0}^{j}2^i = \sum_{j=0}^{n-1}\left(2^{j+1}-1\right) = 2^{n+1}-2-n$

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