1. Chapter 8 Class 11 Sequences and Series
  2. Serial order wise
  3. Ex 8.2
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Ex 8.2, 23 - Chapter 8 Class 11 Sequences and Series

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Ex 8.2, 23 If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P2 = (ab)n. Let a be the first term of G.P & r be the common ratio of G.P Given, first term of G.P = a We know that nth term of G.P = arn-1 b = arn-1 Now P is the product of n terms P = a1 a2 a3 an = a ar ar2 ar3 arn 1 = (a a a) (r r2 rn 1) = an ^(1+2+ +( 1)) = an ^(( ( 1))/2) Thus, P = an ^(( ( 1))/2) We need to prove P2 = (ab)n. Taking L.H.S P2 = ("an " r^((n(n 1))/2) )^2 = ( ^( 2) " " r^((n(n 1))/2 2) ) = ( ^2 " " r^(n(n 1)) ) = ( ^2 " " r^((n 1)) )^ = ( r^((n 1)) )^ = ( ( r^((n 1) )))^ = ( )^ = ( )^ = R.H.S Thus, P2 = ( )^ Hence proved
  1. Chapter 8 Class 11 Sequences and Series
  2. Serial order wise

    3. Ex 8.2

    Examples →
Examples →
Chapter 8 Class 11 Sequences and Series
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo