Last updated at March 9, 2017 by Teachoo

Transcript

Ex 9.2 , 15 If (๐^๐ + ๐^๐)/(๐^(๐โ1) + ๐^(๐โ1) ) 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 (๐^๐ + ๐^๐)/(๐^(๐โ1) + ๐^(๐โ1) ) So, (๐^๐ + ๐^๐)/(๐^(๐โ1) + ๐^(๐โ1) ) = (a + b)/2 2(an + bn) = (a + b) (an โ 1 + bn โ 1) 2an + 2bn = a(an โ 1 + bn โ 1) + b(an โ 1 + bn โ 1) 2an + 2bn = aan โ 1 + abn โ 1 + ban โ 1 + bbn โ 1 2an + 2bn = a1 . an โ 1 + abn โ 1 + ban โ 1 + b1 . bn โ 1 2an + 2bn = a1 + n โ 1 + abn โ 1 + ban โ 1 + b1 + n โ 1 2an + 2bn = a1 + n โ 1 + abn โ 1 + ban โ 1 + b1 + n โ 1 2an + 2bn = an + abn โ 1 + ban โ 1 + bn 2an + 2bn โ an โ abn โ 1 โ an โ 1 b โ bn = 0 2an โ an + 2bn โ bn - abn โ 1 โ an - 1 b = 0 an + bn โ abn โ 1 โ an โ 1 b = 0 an โ an โ 1 b + bn โ a bn โ 1 = 0 a.an โ 1 โ an โ 1 b + b.bn โ 1 โ a bn โ 1 = 0 an โ 1 (a โ b) โ bn โ 1 (a โ b) = 0 (an โ 1 โ bn โ 1)(a โ b) = 0 โด an โ 1 โ bn โ 1 = 0 Solving an โ 1 = bn โ 1 an โ 1 = bn โ 1 ๐^(๐ โ1)/(๐^(๐ โ1) ) = 1 (๐/๐)^(๐ โ1) = 1 (๐/๐)^(๐ โ1) = (๐/๐)^0 Comparing powers n โ 1 = 0 n = 1 Hence n = 1

Chapter 9 Class 11 Sequences and Series

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.