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Induction has three main parts.
Part 1: Prove a base of induction. Choose a base case and prove that the hypothesis holds true for that base case.
Part 2: Induction step. Assume that the induction hypothesis holds true for some natural number $n$.
Part 3: Using the assumption that the induction hypothesis holds true, prove that the hypothesis holds true for $n+1$.
When the problem itself involves "n" I prefer to use "it is true for n= k" and then prove "it is true for k+1", using "k" rather than "n". That way people do not confuse the "induction hypothesis" with the proposition to be proved.