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How to come from this equation to

$ \sum_{i=0}^n k = {n(n+1)\over 2} + (n+1) $

this equation:

$ \sum_{i=0}^n k = {(n+1)(n+2)\over 2} $

Thanks in advance for your answer!

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    As stated this is not correct. $\sum_{i=0}^nk$ should be replaced by $\sum_{k=0}^{n+1}k$ everywhere.2012-12-10

1 Answers 1

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$\sum_{i=0}^{n}k=\frac{n(n+1)}{2}+(n+1)=\frac{n(n+1)}{2}+\frac{2(n+1)}{2}=\frac{n(n+1)+2(n+1)}{2}=\frac{(n+2)(n+1)}{2}$