Pre-calculus assignment

[PlanetRocker]

Hey guys. Ok I have a precalculus assignment and I got the first part but I am completly lost on the second part and was wondering if anyone else could get it. The question is:
Consider the series below:
2 x 3 + 3 x 4 + 4 x 5 + .....+ tn=Sn
i) Find an expression for the nth term in the series in terms of n (tn)
ii) Using the method of finite differences find an experssion for the sum of n terms in the series (Sn) in terms of n (Hint: find S1, S2, S3....and then subtract until you find a common differnece)
iii) Prove that your expression for Sn holds true for all values of "n" where n is an element of the natural numbers.

For part i) I got tn=(n+1)(n+2)
Part ii) is where I get lost. I did the finite differneces and sutff but I just...can't do it. So if anyone has any idea, any help would be apperciated. Thanks alot.

 

[arthur ohlsten]

first differencesn second diff.

S1=[n+1][n+2]=n^2+3n+2........
S2=[n+2][n+3]=n^2+5n+6........ 2n+4................
S3=[n+3][n+4]=n^2+7n+12.......2n+6.................... 2
S4={n+4][n+5}=n^2+9n+20......2n+8................... 2

second differences is a constant 2
the ..... are just to keep format , has nothing to do with the work
Arthur