Mathematical induction: how it works and why.

I give a kind of "mechanical" picture of how induction works, along with some comments about P(n) statements, base case and induction step. Then I prove the validity of induction using proof by contradiction. Finally we have an application of induction to a problem that's nothing like summing up terms of a series (the usual induction examples we see.)
AM-GM proved by induction:
• AM-GM inequality proof...
• The precursor to AM-GM.

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