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1.18 Remarks on induction proofs

(i) Start by stating P(n)P(n), since this may not be obvious to the reader.

(ii) Do not multiply out expressions unless there is no other option.

(iii) Take out for common factors instead. The last step of the calculation should be P(n+1)P(n+1), so this should suggest which factors to look for.

(iv) The target is P(n+1)P(n+1).