  == proof outline ==  It is possible to write down this formula: : This is an alternative way to group the sum of the squares: to quote an example, we assume n=5: : : : : : : In this representation the number five is summed 5 times, the number 4 is summed 4 times, and so on, until zero. After that, it is possible to use this result to solve the summation: : The main formula is equivalent to : After some agebraic manipulation it is possible to obtain: : This is equivalent to the desired formula.    