Give a story proof of the identity 13 ± ± + n3 = 6(n + + 6(// XXXXXXXXXX 2 It is then just basic algebra (not required for this problem) to check that the square of the right-hand side in (a) is the...

Give a story proof of the identity
13 ± ± + n3 = 6(n + + 6(// + 1) 4 3
2
It is then just basic algebra (not required for this problem) to check that the square of the right-hand side in (a) is the right-hand side in (b). Hint: Imagine choosing a number between 1 and n and then choosing 3 numbers between 0 and n smaller than the original number, with replacement. Then consider cases based on how many distinct numbers were chosen.