Question 9 - Miscellaneous - Chapter 8 Class 11 Sequences and Series

Last updated at April 16, 2024 by

Misc 16 - If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are AP - Arithmetic Progression (AP): Calculation based/Proofs

Misc 16 - Chapter 9 Class 11 Sequences and Series - Part 2

Transcript

Misc 16 If a(1/( ) " + " 1/ ), b(1/ " + " 1/ ), c(1/ " + " 1/ ) are in AP., prove that a, b, c are in AP Given that a(1/( ) " + " 1/ ), b(1/ " + " 1/ ), c(1/ " + " 1/ ) are in AP. If a(1/( ) " + " 1/ ), b(1/ " + " 1/ ), c(1/ " + " 1/ ) are in AP Adding 1 to each term a(1/( ) " + " 1/ ) + 1, b(1/ " + " 1/ ) + 1, c(1/ " + " 1/ ) + 1 are in AP a(1/( ) " + " 1/ ) + / , b(1/ " + " 1/ ) + / , c(1/ " + " 1/ ) + / are in AP a (1/( ) " + " 1/ " + " 1/ ) , b(1/ " + " 1/ " + " 1/( )) , c(1/ " + " 1/( ) " + " 1/ ) are in AP Divide each term by (1/ " + " 1/( ) " + " 1/ ) (1/( ) " + " 1/ " + " 1/ )/(1/ " + " 1/( ) " + " 1/ ), (1/ " + " 1/ " + " 1/( ))/(1/ " + " 1/( ) " + " 1/ ), (1/ " + " 1/( ) " + " 1/ )/(1/ " + " 1/( ) " + " 1/ ) are in AP a, b, c are AP Hence, a, b, c, are in AP Hence proved

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.