Question: 1. We know that 1 = 1. It turns out that 2+3+4 = 1+8 and that 5+6+7+ 8+9 = 8+27 and that 10+11+12+13+14+15+16 = 27+64. Does this generalize? Write out a general form for the pattern this follows, and then either give a counterexample or a proof.
2. Which two of the previous problems give different ways of counting the same quantity?