Proof By Induction

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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.


To prove that something is true for all integers $n{\ge}r$ :


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