In this video I go through another problems plus example which in this case is on Mathematical Induction. I also go over mathematical induction is and use the tough problems plus example to illustrate it further. The principle of mathematical induction is pretty straight forward but the wording of it can be a bit tricky. Basically it states that if your function is true for n = 1, and it's true for k+1 if at k is true then it is true for all positive integers n. Since n = 1 is true, it follows that n = 2 is true and thus n = 3 and so on forever.

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Problems Plus – Example 4 – Mathematical Induction

Principle of Mathematical Induction

Let S_n be a statement about the positive integer n.

Suppose that:

1. S₁ is true.
2. S_k+1 is true whenever S_k is true.

Thus S_n is true for all positive integers n.

Example

Solution