Question

According to principle of mathematical induction, if P(k+1) = m^(k+1) + 5 is true then _____ must be true.

(a) P(k) = 3m^(k)

(b) P(k) = m^(k) + 5

(c) P(k) = m^(k+2) + 5

(d) P(k) = m^(k)

I had been asked this question in an interview for job.

The above asked question is from Principle of Mathematical Induction in division Induction and Recursion of Discrete Mathematics

Answer 1

Correct choice is (b) P(k) = m^(k) + 5

The best I can explain: By the principle of mathematical induction, if a statement is true for any number m = k, then for its successor m = k + 1, the statement also satisfies, provided the statement is true for m = 1. So, the required answer is p(k) = m^k + 5.