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IAT IISER2018MathematicsMathematical Induction

Let (P(n) ) be a statement for each natural number (n ). Assume that (P(n+1) ) is a true statement whenever (P(n) ) is a true statement. Suppose (P(2018) ) is true. Then which one of the following statements is true?

Options

  1. A(P(n) ) is true for exactly two values of (n ).
  2. B(P(n) ) is false for at most finitely many values of (n ).
  3. C(P(n) ) is false for infinitely many values of (n ).
  4. D(P(n) ) is true for all (n ).

Correct answer

B. (P(n) ) is false for at most finitely many values of (n ).

Step-by-step solution

No solution available.

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