1. Summing - question

Hey guys, just a quick query. The question says:

Find, as polynomials in n, the sum of

1.2.3 + 2.3.4 + ..... + n(n+1)(n+2)

__________________________________________________ _____

Is that simply

$\displaystyle \Sigma_{k=1}^{n} k(k+1)(k+2) = \Sigma_{k=1}^{n} k^3 + 3 \Sigma_{k=1}^{n} k^2 + 2 \Sigma_{k=1}^{n} k$

which, skipping through the steps is:

$\displaystyle \frac{1}{4}n(n+1)(n+2)(n+3)$

This is what they're asking for, aren't they?

2. Originally Posted by WWTL@WHL
Hey guys, just a quick query. The question says:

Find, as polynomials in n, the sum of

1.2.3 + 2.3.4 + ..... + n(n+1)(n+2)

__________________________________________________ _____

Is that simply

$\displaystyle \Sigma_{k=1}^{n} k(k+1)(k+2) = \Sigma_{k=1}^{n} k^3 + 3 \Sigma_{k=1}^{n} k^2 + 2 \Sigma_{k=1}^{n} k$

which, skipping through the steps is:

$\displaystyle \frac{1}{4}n(n+1)(n+2)(n+3)$

This is what they're asking for, aren't they?
yes, provided you made no mistakes in your "skipping through the steps" section, that is what they're after. you could probably expand it though, so it is in somewhat more of a standard form

3. Yes, that is exactly what they want.

4. Fantastic. Just making sure, since this is worded a lot differently from when I encountered similar questions at school.

Thanks guys.