square pyramidal numbers proof 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 86 24 46 135