Deriving the formula of a summation Derive the formula for 
$$
\sum_{k=1}^n k^2
$$
The solution's that I was given has $k^3 + (k-1)^3$ as the first step but doesn't say how it got to that.  Any help?

Hint:
For nonnegative integers $n,r$ with $r\leq n$ it is surprisingly
easy to prove by induction that 

$\sum_{k=r}^{n}\binom{k}{r}=\binom{n+1}{r+1}$ 

This result allows you to find formulas for $\sum_{k=1}^{n}k^{r}$
for $r=1,2,3,\ldots$
