


Subscribe to our Youtube Channel - https://you.tube/teachoo
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, 2 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 3 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 4 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 5 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 6 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 7 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 8 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 9 Not in Syllabus - CBSE Exams 2021 You are here
Ex 4.1, 10 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 11 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 12 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 13 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 14 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 15 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 16 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 17 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 18 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 19 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 20 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 21 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 22 Not in Syllabus - CBSE Exams 2021
Ex 4.1, 23 Important Not in Syllabus - CBSE Exams 2021
Ex 4.1, 24 Important Not in Syllabus - CBSE Exams 2021
About the Author