Question

State the second principle of mathematical induction.

Answer 1

Let M be an integer. Suppose we want to prove that P(n) is true for all positive integers ≥M. Then if we show that: 

Step 1: P(M) is true, and 

Step 2: for an arbitrary positive integer k≥M, if P(M).P(M+1).P(M+2)……P(k) are true then P(k+1) is true, 

Then P(n) is true for all positive integers greater than or equal to M.