Help with sequence needed.

[/\/\isanThr0p]

Hey everyone I am looking for a formular that works for this sequence...
1*2 + 2*3 + 3*4 + ... + n(n+1).

thanks!

[wy125]

If you take a close you'll see that your series is:


1^2 + 1 + 2^2 + 2 + ... + n^2 + n

So, separate the terms and write it like this



S = 1 + 2 + 3 + ... n + 1^2 + 2^2 + ... n^2


So it's just the sum of all integers from 1 to n plus the sum of all squares from 1 to n.

S = n(n+1)/2 + n(n+1)(2n+1)/6

[/\/\isanThr0p]

great!!!
Thanks!!!!

[Guv]

Wy125: You deserve a Bravo! & an Ole! Nice analysis.

[/\/\isanThr0p]

yeah and fast!!
thanks a lot again

now I have to prove it with induktion oh well I guess I am gonna do that tomorrow

[wy125]

no problem. guv, thanks for the praise but I'm much more impressed with your polynomial roots program!

[/\/\isanThr0p]

haha seems like I ran over two math freaks... I guess I am gonna add you to my buddy list...
any of you guys got ICQ? I could really need some kind of math expert there...

[sql_lall]

Just to tidy it up a bit:
n(n+1)/2 + n(n+1)(2n+1)/6
=
3n(n+1)/6 + n(n+1)(2n+1)/6
=
(3n(n+1) + n(n+1)(2n+1))/6
=
n(n+1)(2n+4)/6
=
n(n+1)(n+2)/3

-N.B. this also equals: (n^3 + 2n^2 + n)/3

[/\/\isanThr0p]

For stuff like that I use my TI 92+ (well sometimes my brain, only a few times though)
thanks anyways