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Maths question help!!!

What would the common difference be in a series represented like this:
and how would I calculate this?
5
Σ r(r+1)
r=0
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B_9710
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Original post by Purpleunicorn197
What would the common difference be in a series represented like this:
and how would I calculate this?
5
Σ r(r+1)
r=0


There is no common difference like with a geometric series. But you can split the summation up as follows
∑r=0nr(r+1)=∑r=0nr2+∑r=0nr \displaystyle \sum_{r=0}^n r(r+1) = \sum_{r=0}^n r^2 + \sum_{r=0}^n r .
Using the standard results
∑r=1nr2=16n(n+1)(2n+1) \displaystyle \sum_{r=1}^n r^2 = \frac{1}{6} n(n+1)(2n+1) and
∑r=1nr=12n(n+1) \displaystyle \sum_{r=1}^n r = \frac{1}{2} n(n+1) .
Remember that for the sum you gave we start at r=0, not 1.

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