Example 1

In this video I show you how to use mathematical induction to prove the sum of the series

Prove the following:

  1. \sum\limits_{r = 1}^n {{2^r} = 2{^{n + 1}} - 2}

The method of induction:

  • Start by proving that it is true for n=1, then assume true for n=k and prove that it is true for n=k+1. If so it must be true for all positive integer values of n.
Induction - Sum of series : Example 1 : ExamSolutions - youtube Video

Example 2

In this video I show you how to use mathematical induction to prove the sum of the series

Prove the following:

  1. \sum\limits_{r = 1}^n {{4^{r - 1}} = \dfrac{{{4^n} - 1}}{3}}
Induction - Sum of series : Example 2 : ExamSolutions - youtube Video