Why is $\displaystyle

\sum^{n}_{r=1}(4r^2-4r+1)=4\sum^{n}_{r=1}r^2-4\sum^{n}_{r=1}r+\sum^{n}_{r=1}1 ??

$

It looks like expansion but i don think it is ...

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- Feb 2nd 2009, 08:04 AMmathaddictsummation
Why is $\displaystyle

\sum^{n}_{r=1}(4r^2-4r+1)=4\sum^{n}_{r=1}r^2-4\sum^{n}_{r=1}r+\sum^{n}_{r=1}1 ??

$

It looks like expansion but i don think it is ... - Feb 2nd 2009, 08:17 AMo_O
These properties hold for summations:

- $\displaystyle \sum_{k = 1}^n \left(a_k \pm b_k\right) = \sum_{k=1}^n a_k \pm \sum_{k=1}^n b_k$
- $\displaystyle \sum_{k = 1}^n ca_k = c\sum_{k=1}^n a_k$ where $\displaystyle c$ is a constant

See how these apply to your summation?