Equal - 1 upon addition
Example 3 Deleted for CBSE Board 2024 Exams
Question 11 Important Deleted for CBSE Board 2024 Exams
Question 10 Deleted for CBSE Board 2024 Exams
Question 16 Important Deleted for CBSE Board 2024 Exams
Question 17 Important Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams
Equal - 1 upon addition
Last updated at April 16, 2024 by Teachoo
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 + ....+ 1/2𝑘 = 1 – 1/2𝑘 We will prove that P(k + 1) is true. R.H.S = 1 – 1/2^(𝑘 + 1) L.H.S = 1/2 + 1/4 + 1/8 + ....+ 1/2^(𝑘 + 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