Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Chapter 9 Class 11 Sequences and Series
Question 5 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 15 Important Deleted for CBSE Board 2024 Exams You are here
Question 17 Deleted for CBSE Board 2024 Exams
Example 9 Important
Example 10 Important
Ex 8.2, 3 Important
Ex 8.2, 11 Important
Ex 8.2, 17 Important
Ex 8.2, 18 Important
Ex 8.2, 22 Important
Ex 8.2, 28
Ex 8.2, 29 Important
Ex 9.4.4 Important Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 10 Deleted for CBSE Board 2024 Exams
Question 9 Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Misc 10 Important
Question 13 Important Deleted for CBSE Board 2024 Exams
Misc 14 Important
Misc 18 Important
Chapter 9 Class 11 Sequences and Series
Last updated at May 29, 2023 by Teachoo
Ex 9.2 , 15 If (𝑎^𝑛 + 𝑏^𝑛)/(𝑎^(𝑛−1) + 𝑏^(𝑛−1) ) is the A.M. between a and b, then find the value of n. We know that arithmetic mean between a & b is A.M. = (a + b)/2 It is given that AM between a & b is (𝑎^𝑛 + 𝑏^𝑛)/(𝑎^(𝑛−1) + 𝑏^(𝑛−1) ) So, (𝑎^𝑛 + 𝑏^𝑛)/(𝑎^(𝑛−1) + 𝑏^(𝑛−1) ) = (a + b)/2 2(an + bn) = (a + b) (an – 1 + bn – 1) 2an + 2bn = a(an – 1 + bn – 1) + b(an – 1 + bn – 1) 2an + 2bn = aan – 1 + abn – 1 + ban – 1 + bbn – 1 2an + 2bn = a1 . an – 1 + abn – 1 + ban – 1 + b1 . bn – 1 2an + 2bn = a1 + n – 1 + abn – 1 + ban – 1 + b1 + n – 1 2an + 2bn = a1 + n – 1 + abn – 1 + ban – 1 + b1 + n – 1 2an + 2bn = an + abn – 1 + ban – 1 + bn 2an + 2bn – an – abn – 1 – an – 1 b – bn = 0 2an – an + 2bn – bn - abn – 1 – an - 1 b = 0 an + bn – abn – 1 – an – 1 b = 0 an – an – 1 b + bn – a bn – 1 = 0 a.an – 1 – an – 1 b + b.bn – 1 – a bn – 1 = 0 an – 1 (a – b) – bn – 1 (a – b) = 0 (an – 1 – bn – 1)(a – b) = 0 ∴ an – 1 – bn – 1 = 0 Solving an – 1 = bn – 1 an – 1 = bn – 1 𝑎^(𝑛 −1)/(𝑏^(𝑛 −1) ) = 1 (𝑎/𝑏)^(𝑛 −1) = 1 (𝑎/𝑏)^(𝑛 −1) = (𝑎/𝑏)^0 Comparing powers n – 1 = 0 n = 1 Hence n = 1