Check sibling questions

Mathematical Induction - Questions and Solutions

ExamplesΒ β†’
Mathematical Induction
Serial order wise

Question 9 - Mathematical Induction - Questions and Solutions - Mathematical Induction

Last updated at May 29, 2023 by

Ex 4.1, 9 - Prove 1/2 + 1/4 + 1/8 + ... + 1/2n = 1 - 1/2n - Ex 4.1

Ex 4.1, 9 - Chapter 4 Class 11 Mathematical Induction - Part 2
Ex 4.1, 9 - Chapter 4 Class 11 Mathematical Induction - Part 3 Ex 4.1, 9 - Chapter 4 Class 11 Mathematical Induction - Part 4

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

Transcript

Question 9: Prove the following by using the principle of mathematical induction for all n ∈ N: 1/2 + 1/4 + 1/8 + ....+ 1/2𝑛 = 1 – 1/2𝑛 Let P(n): 1/2 + 1/4 + 1/8 + ....+ 1/2𝑛 = 1 – 1/2𝑛 For n = 1, we have L.H.S = 1/2 R.H.S = 1 – 1/21 = 1/2 Hence, L.H.S. = R.H.S , ∴ P(n) is true for n = 1 Assume P(k) is true 1/2 + 1/4 + 1/8 + ....+ 1/2π‘˜ = 1 – 1/2π‘˜ We will prove that P(k + 1) is true. R.H.S = 1 – 1/2^(π‘˜ + 1) L.H.S = 1/2 + 1/4 + 1/8 + ....+ 1/2^(π‘˜ + 1) L.H.S = R.H.S ∴ P(k + 1) is true whenever P(k) is true. ∴ By the principle of mathematical induction, P(n) is true for n, where n is a natural number

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.