Check sibling questions

Ex 9.3, 27 - Find value of n so that an+1 + bn+1 / an + bn - Ex 9.3

Ex 9.3, 27 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.3, 27 - Chapter 9 Class 11 Sequences and Series - Part 3

This video is only available for Teachoo black users


Transcript

Ex9.3, 27 Find the value of n so that (𝑎^(𝑛 + 1) +𝑏^(𝑛 + 1))/(𝑎^(𝑛 ) +𝑏^𝑛 ) may be the geometric mean between a and b. We know that geometric mean between a & b is a & b = √ab It is given that G.M. between a & b = (𝑎^(𝑛 + 1) +𝑏^(𝑛 + 1))/(𝑎^(𝑛 ) +𝑏^(𝑛 ) ) √ab = (𝑎^(𝑛 + 1) +𝑏^(𝑛 + 1))/(𝑎^(𝑛 ) +𝑏^(𝑛 ) ) 〖"(ab)" 〗^(1/2) = (𝑎^(𝑛 + 1) +𝑏^(𝑛 + 1))/(𝑎^(𝑛 ) +𝑏^(𝑛 ) ) 〖"(ab)" 〗^(1/2) (an +bn) = an + 1 + bn + 1 〖"a" 〗^(1/2) 𝑏^(1/2) (an +bn) = an + 1 + bn + 1 〖"a" 〗^(1/2) an 𝑏^(1/2) + 〖"a" 〗^(1/2) bn 𝑏^(1/2) = an + 1 + bn + 1 𝑎^(1/2 + 𝑛 ) 𝑏^(1/2) + 〖"a" 〗^(1/2) 𝑏^(1/2 + 𝑛 )= an + 1 + bn + 1 𝑎^(1/2 + 𝑛 ) 𝑏^(1/2) – an + 1 = bn + 1 – 〖"a" 〗^(1/2) 𝑏^(1/2 + 𝑛 ) 𝑎^(1/2 + 𝑛 ) 𝑏^(1/2) – 𝑎^(𝑛 + 1/2 + 1/2) = 𝑏^(𝑛 + 1/2 + 1/2) – 𝑎^(1/2) 𝑏^(1/2 + 𝑛 ) 𝑎^(1/2 + 𝑛 ) [𝑏^(1/2) – 𝑎^(1/2)] = 𝑏^(𝑛 + 1/2 ) [𝑏^(1/2) – 𝑎^(1/2)] 𝑎^(1/2 + 𝑛 )= 𝑏^(𝑛 + (1 )/2 "[" 𝑏^(1/2) " − " 𝑎^(1/2) "] " )/(𝑏^(1/2) " − " 𝑎^(1/2) ) 𝑎^(1/2 + 𝑛 )= 𝑏^(𝑛 +1/2) (𝑎/𝑏)^(1/2 + 𝑛) = 1 (𝑎/𝑏)^(1/2 + 𝑛)= (𝑎/𝑏)^0 Comparing powers 1/2 + n = 0 n = – 1/2 Hence value of n is - 1/2

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.