My Math Forum Using series manipulations to find the sums of finite series

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 April 22nd, 2016, 01:17 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 03:25 PM.
 April 22nd, 2016, 01:40 PM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 2,940 Thanks: 1544 $\displaystyle \sum_{k=21}^{44} \left(\dfrac{k^3}{6} - 2k^2\right) = \displaystyle \dfrac{1}{6} \sum_{k=21}^{44} k^3 - 2\sum_{k=21}^{44} k^2$ also, note ... $\displaystyle \sum_{k=21}^{44} a_n = \sum_{k=1}^{44} a_n - \sum_{k=1}^{20} a_n$ Thanks from stevewilliams

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