Quick series question

1. Oct 3, 2007

iamaelephant

Hi, I'm just going through an example of closed forms of series in a text book (Anton Calc) and I'm wondering how they got to this step, can someone please explain it to me? Also, any hints on formulating closed forms would be greatly appreciated, they are not covered in detail in my text. Thanks a lot!

1. The problem statement, all variables and given/known data

$$\sum_{k=o}^{3+n}{k^2} - 14 =\frac{(3+n)(4+n)(7+2n)}{6} - 14$$

Sorry if it's a stupid question, but I've never tried working with a sum with variable at the top, and I don't know what I'm doing.

2. Relevant equations
Given above

3. The attempt at a solution
None, this is an example problem I don't understand.

Edit - there should be brackets surrounding the sum that cut off the -14 as it's not part of the sum. I couldn't work this out in LaTeX and I'm in a hurry.

2. Oct 3, 2007

real10

the first part is the sum of first x squares (in this case x = 3+n)
$$\sum_{k=o}^{x}{k^2} = \frac{x(x+1)(2x+1)}{6}$$ plug in x= 3+n then u get
$$\frac{(3+n)(4+n)(7+2n)}{6}$$
of course u can prove these sums to the first "x" terms of k^n (in ur case it is k^2)..

3. Oct 4, 2007

iamaelephant

Thanks a lot! Heh, always seems so simple when someone explains it :)

4. Oct 4, 2007

iamaelephant

Is anyone able to give me some hints or links on how to find the closed form of any series? I'm really stuck here and my text books don't seem to cover it.