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why does in PMI(principle of mathematical induction) in many books solved the answers for P(1) true.even though P(2) and etc not true.And finally given the conclusion n true for all N.

why does in PMI(principle of mathematical induction) in many books solved the answers for P(1) true.even though P(2) and etc not true.And finally given the conclusion n true for all N.

Grade:11

1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
7 years ago
Hi,

After solving for P1 you have to look out for Pn and Pn+1 to generalize.
Why we do the generalization is because it may be the case that P1 holds but P2 and P3 may not. So checking for any number n and no just next to it i.e. n+1 will generalize the formula.
So just checking for P1 is obviously incorrect method.

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