Mathematical Induction Conclusion

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Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if

(i) it holds for n = 1 and

(ii) it holds for n = k+1 whenever it holds for n = k.

Remember:

Proof by mathematical induction requires the fulfilment of both the conditions (i) and (ii) as stated above.

Condition (i) creates the basis for carrying out induction and condition (ii) gives us the right to make a general assertion or of an automatic extension.