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$$3*\sum_{k=2}^{25}{k^2} + 2*\sum_{k=2}^{24}{k}- \sum_{k=0}^{25}{1}$$

I asked a different summation question before, I wanted to see If I got the hang of it. So i'm trying to write this as 1 summation with added/subtracted extra terms if needed.

I made my k=2 in all of the summations and the upper index be 25.

$2*\sum_{k=2}^{24}{k}$ = $2*\sum_{k=2}^{25}{k} +(2*-25)$

$- \sum_{k=0}^{25}{1}$ = $- \sum_{k=2}^{25}{1}-(+1+1)$

So Finally I got $$\sum_{k=2}^{25}{3k^2 +2k-1} $$ subtract 52 from the whole sum.

Is this correct?

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1 Answer 1

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\begin{align}3\sum_{k=2}^{25}{k^2} + 2\sum_{k=2}^{24}{k}- \sum_{k=0}^{25}{1} &= 3\sum_{k=2}^{25}{k^2} + 2\left(\sum_{k=2}^{25}{k}-25\right)- \left(\sum_{k=2}^{25}{1}\right)-2\\ &=\left[\sum_{k=2}^{25}(3k^2+2k-1)\right] -52 \end{align}

Yes, using braces helps.

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