Geometric Series Question Variable answer

Question

I'm having a bit of trouble with the answer for this question. I've found that u1 is 9p, but i cant find the common ratio.

$$\sum_{n=-3}^2{pn^2}=\;?$$

So for my series looks like this:

9p+4p+p+0+p+4p

I can add it to get 19p, but is there a way to use the geometric series formula to find the sum?

What geometric series? The finite sum there is not a geometric one. — DonAntonio, Nov 29 '16 at 06:57
Oh , my mistake then. So is there a way to find the sum with a formula, or do i just have to add each term together. — user392500, Nov 29 '16 at 06:58
Not that I can see: you just have to sum them all up directly, imo. — DonAntonio, Nov 29 '16 at 06:59
@DonAntonio: Actually there is a very well-known formula for $1^2+\dots+n^2$, see here for example: http://math.stackexchange.com/questions/95047/combinatorial-interpretation-of-sum-of-squares-cubes — Hans Lundmark, Nov 29 '16 at 07:41
@HansLundmark I know, but there's no point in using it in cases like this, with so small a number of summands. — DonAntonio, Nov 29 '16 at 09:17
@DonAntonio: Of course, but the question was if you have to do it that way. — Hans Lundmark, Nov 29 '16 at 10:05

score 1 · Answer 1 · answered Nov 29 '16 at 06:58

1

Directly:

$$\sum_{n=-3}^2 pn^2=9p+4p+p+0+p+4p=19p$$

...and that's pretty much all there is. The finite sum above is not a geometric one.

answered Nov 29 '16 at 06:58

DonAntonio

1 Answers1