Ex 4.1, 9 - Chapter 4 Class 11 Mathematical Induction
Last updated at May 29, 2018 by Teachoo
Transcript
Ex 4.1, 9: Prove the following by using the principle of mathematical induction for all n โ N: 1/2 + 1/4 + 1/8 + ....+ 1/2๐ = 1 โ 1/2๐ Let P(n): 1/2 + 1/4 + 1/8 + ....+ 1/2๐ = 1 โ 1/2๐ For n = 1, we have L.H.S = 1/2 R.H.S = 1 โ 1/21 = 1/2 Hence, L.H.S. = R.H.S , โด P(n) is true for n = 1 Assume P(k) is true 1/2 + 1/4 + 1/8 + ....+ 1/2๐ = 1 โ 1/2๐ We will prove that P(k + 1) is true. R.H.S = 1 โ 1/2^(๐ + 1) L.H.S = 1/2 + 1/4 + 1/8 + ....+ 1/2^(๐ + 1) L.H.S = R.H.S โด P(k + 1) is true whenever P(k) is true. โด By the principle of mathematical induction, P(n) is true for n, where n is a natural number
Ex 4.1
Ex 4.1, 1
Important
Ex 4.1, 2
Ex 4.1, 3
Ex 4.1, 4
Ex 4.1, 5
Ex 4.1, 6
Ex 4.1, 7 Important
Ex 4.1, 8
Ex 4.1, 9 You are here
Ex 4.1, 10
Ex 4.1, 11 Important
Ex 4.1, 12
Ex 4.1, 13 Important
Ex 4.1, 14
Ex 4.1, 15
Ex 4.1, 16
Ex 4.1, 17
Ex 4.1, 18
Ex 4.1, 19
Ex 4.1, 20
Ex 4.1, 21 Important
Ex 4.1, 22
Ex 4.1, 23 Important
Ex 4.1, 24
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.