Today’s theme is the principle of mathematical induction.
Recall that induction is a proof technique used to prove that a property P(n) holds for every natural number n, i.e. for n = 1, 2, 3,…
It consists of two parts:
(I) The base case: proving the property for n=1.
(II) The induction step: assuming that we already know the property holds for n=k, we prove it for n=k+1.
There are slight variations of this technique, the most common one being strong induction: for the step, we assume that the property holds for all n less than or equal to k, and then prove it for n=k+1.
Click here for the worksheet.