Question

For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to ________

(a) m^2+3

(b) m+1

(c) m^m

(d) 3m^2+4

The question was posed to me in class test.

Question is taken from Principle of Mathematical Induction topic in division Induction and Recursion of Discrete Mathematics

Answer 1

Right choice is (a) m^2+3

To explain: The required answer is m^2+3. Now, by induction assumption, we have to prove 2+4+6+…+4(k+1) = (k+1)^2+3  also can be true, 2+4+6+…+4(k+1) = 2+4+6+⋯+(4k+4) and by the subsequent steps, we can prove that (m+1)^2+3 also holds for m=k. So, it is proved.