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 \[ 1,~(1+2),~(1+2+2^2),~\dots ~(1+2+2^2+\dots+2^{n1}) \] 
April 29th, 2014, 01:42 PM  #2 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361 
$\displaystyle \sum_{j=0}^{n1}\sum_{i=0}^{j}2^i = \sum_{j=0}^{n1}\left(2^{j+1}1\right) = 2^{n+1}2n$


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