

InterviewSolution
Saved Bookmarks
1. |
For m = 1, 2, …, 4m+2 is a multiple of ________(a) 3(b) 5(c) 6(d) 2This question was addressed to me by my college director while I was bunking the class.Question is from Principle of Mathematical Induction topic in section Induction and Recursion of Discrete Mathematics |
Answer» CORRECT option is (d) 2 Explanation: For n = 1, 4 * 1 + 2 = 6, which is a multiple of 2. Assume that 4m+2 is true for m=k and so 4k+2 is true based on the assumption. Now, to PROVE that 4k+2 is also a multiple of 2 ⇒ 4(k+1)+2 ⇒ 2 * 4k – 4k + 6 ⇒ 2*4k+4 – 4k+2 ⇒ 2(4k+2) – 2(2k+1). Here, the FIRST term 2(4k+2) is true as PER assumption and the second term 2(4k+2) is must to be a multiple of 2. Hence, 4(k+1)+2 is a multiple of 2. So, by induction HYPOTHESIS, (4m+2) is a multiple of 2, for m = 1,2,3,… |
|