Prove i n(n + 1) = 4 i=1 HUGE HINT: There are actually many ways to prove this equation. It reveals a very interesting fact about the relationship between squares and cubes. The easiest way to prove this is to manipulate our normal approach to the Principle of Mathematical Induction. Normally, we check the base case, then assume P(k) is true, and then show that P(k+1) is true. You can do this here but it will require a lot of algebra. What you can instead do is notice that the Principle of Mathematical Induction applies for any two consecutive integers, so you could try assuming that P(k-1) is true, and then show that P(k) is true as k-1 and k are consecutive integers just as k and k +1 are.