Addition Series: Sum of Successive Terms

[rajeshmarndi]

Homework Statement

I want to have a formula of this kind,
(8+7+...+1) + (7+6+..+1) + (6+5+..+1) + ...1

Homework Equations

The Attempt at a Solution

I know , n+(n-1)+...+1 = n(n+1)/2

 

[Svein]

So you want a formula for $\frac{n(n+1)}{2}+\frac{(n-1)n}{2}+...$, or $\sum_{k=1}^{n}\frac{k(k+1)}{2}=\frac{1}{2}\sum_{k=1}^{n}(k(k+1))=\frac{1}{2}(\sum_{k=1}^{n}k^{2}+\sum_{k=1}^{n}k)$.