Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Ex 8.2

Ex 8.2, 1

Ex 8.2, 2

Ex 8.2, 3 Important

Ex 8.2, 4

Ex 8.2, 5 (a)

Ex 8.2, 5 (b) Important

Ex 8.2, 5 (c)

Ex 8.2, 6

Ex 8.2, 7 Important

Ex 8.2, 8

Ex 8.2, 9 Important

Ex 8.2, 10

Ex 8.2, 11 Important

Ex 8.2, 12

Ex 8.2, 13

Ex 8.2, 14 Important

Ex 8.2, 15

Ex 8.2, 16 Important

Ex 8.2, 17 Important

Ex 8.2, 18 Important

Ex 8.2, 19

Ex 8.2, 20

Ex 8.2, 21

Ex 8.2, 22 Important

Ex 8.2, 23 Important

Ex 8.2, 24

Ex 8.2, 25

Ex 8.2, 26 Important

Ex 8.2, 27 Important You are here

Ex 8.2, 28

Ex 8.2, 29 Important

Ex 8.2, 30 Important

Ex 8.2, 31

Ex 8.2, 32 Important

Chapter 8 Class 11 Sequences and Series

Serial order wise

Last updated at May 29, 2023 by Teachoo

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