# 1.15

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Call the statement and the general term

**Step 1:** Show that the statement holds for the basis case

Since , the basis case is true.

**Step 2:** Assume that holds.

**Step 3:** Show that on the assumption that the summation is true for *k*, it follows that it is true for *k + 1*.

It's easier to factor than expand. Notice the common factor of *(k + 1)(k + 2)(k + 3)*.

This should be equal to the formula
when *k = k + 1*:

Since both the basis and the inductive step have been proved, it has now been proved by mathematical induction that S_n holds for all natural n.

Back to Chapter 1.