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  • Principle of Mathematical Induction:
Corresponding to each positive integer n let there be a statement or a proposition P(n).
If    (i) P(1) is true, and
      (ii) P(k+1) is true wherever P(k) is true, [Where k is a positive integer]
Then P(n) is true for all positive integers n.
  • Working rules for using principle of mathematical induction:
Step (1) : Show that the result is true for n = 1.
Step (2) : Assume the validity of the result for n equal to some arbitrary but fixed natural number, say k.
Step (3) : Show that the result is also true for n = k + 1.
Step (4) : Conclude that the result holds for all natural numbers.

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