Question

State whether the following series is true or not.

(a) }{2}\)

(b) True

(c) False

This question was posed to me in exam.

My doubt is from The Principle of Mathematical Induction topic in division Principle of Mathematical Induction of Mathematics – Class 11

Answer 1

Right option is (a) }{2}\)

For explanation: P(n) = n(n + 1)/2

P(1) = 1

We assume P(k) to be true, therefore, P(k) = \(\frac{k(k + 1)}{2}\)

To prove that, P(k + 1) = \(\frac{(k+1)(k+ 2)}{2}\)

Proof:

P(k + 1) = 1 + 2 + 3 +….+ k + k + 1

P(k + 1) = \(\frac{k(k + 1)}{2}\) + k+1

P(k + 1) = \(\frac{k(k+ 1)+2(k+1)}{2}\)

P(k + 1) = \(\frac{(k+1)(k+ 2)}{2}\)

Therefore, P(n) is true by principle of mathematical induction.