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April 22nd, 2016, 02:17 PM  #1 
Newbie Joined: Apr 2016 From: newcastle Posts: 14 Thanks: 0  Using series manipulations to find the sums of finite series
Hi Quick question I'm having difficultly with, if I have a problem like this, finding the sum of finite series Then I can use this formula But if I have a question like this Can I still just use this formula Or do I have to add on this formula to the second part Any help is greatly appreciated. Thanks, Steve Last edited by skipjack; April 30th, 2016 at 04:25 PM. 
April 22nd, 2016, 02:40 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,805 Thanks: 1449 
$\displaystyle \sum_{k=21}^{44} \left(\dfrac{k^3}{6}  2k^2\right) = \displaystyle \dfrac{1}{6} \sum_{k=21}^{44} k^3  2\sum_{k=21}^{44} k^2$ also, note ... $\displaystyle \sum_{k=21}^{44} a_n = \sum_{k=1}^{44} a_n  \sum_{k=1}^{20} a_n$ 

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find, finite, manipulations, series, sums 
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