Induction

Induction is used in a math as a technique for proving differenct concepts and theories. The process is divided into three steps: base case(s), induction hypothesis, and the induction step.

Examples

Sum of Counting Numbers

For example, say we have a formula that describes the partial sum of the counting numbers. Shown below is the partial sum for the sequence of the first 1, 2, 3, and n counting numbers.

This formula is given in the form and now we want to prove that the formula holds true for all possible numbers .

Say we have found a formula that

describes the pattern for the series of counting numbers given by the equation below.

The sequence of -th terms is represented as

The sequence of partial sums is represented as