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April 22nd, 2016, 02:17 PM   #1
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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.
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April 22nd, 2016, 02:40 PM   #2
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$\displaystyle \sum_{k=21}^{44} \left(\dfrac{k^3}{6} - 2k^2\right) = \displaystyle \dfrac{1}{6} \sum_{k=21}^{44} k^3 - 2\sum_{k=21}^{44} k^2$

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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