1.

State whether the following series is true or not.(a) }{2}\)(b) True(c) FalseThis 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»

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.


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