# Proof By Induction

Proof by induction is a proof made by first assuming that a statement is true for a general case (i.e. when $n=k$ ), then proving that it still holds true for the next case (i.e. when $n=k+1$ ) and then proving that it is true for the first (base) case; if the statement does hold for both the base case and the inductive step ( $n=k+1$ ), then, by induction, the statement must be true.

## METHOD

To prove that something is true for all integers $n{\ge}r$ :
• assume that it is true for $n=k$
• prove that it remains true for $n=k+1$
• prove that it is true for $n=r.$

## Examples

It would be nice to have some small, clean examples here. Not too many, not too much.