Question: Let S(n) = 1 + 2 + . . . n be the sum of the first n natural numbers and let C(n) = 1³ + 2³ + . . . n³ be the sum of the first n cubes.
Prove the following equalities by induction on n, to arrive at the curious conclusion C(n) = S²(n) for every n. a.
S(n) = ½n(n+1) b.
C(n) = ¼(n4 + 2n³ + n²) = ¼n²(n+1)²
You have to assure the requirements specified in the instruction.