Proof by Induction

Proof by mathematical induction

used to prove the truth of statements that hold for natural numbers n = 1,2,3...

2 steps

@todo

Proof by induction

Proof by induction is a powerful technique to prove mathematical statements of the form ‘for all integers n ge 1, p open bracket n close bracket is true’, where p open bracket n close bracket is some mathematical proposition depending on n. A proof by induction has two steps:

Step 1 Prove that p open bracket 1 close bracket is true.

Step 2 Prove that if p open bracket k close bracket is true for some general k, then p open bracket k+1 close bracket must also be true.

It then follows that for any particular value k, p open bracket k close bracket must be true: by Step 1, p open bracket 1 close bracket is true; so, by Step 2 with n=1, p open bracket 2 close bracket is true; then, by Step 2 with n=2, p open bracket 3 close bracket is true; and so on.