Ex 8.2, 29 - Chapter 9 Class 11 Sequences and Series (Important Question)
Last updated at April 16, 2024 by Teachoo
Chapter 9 Class 11 Sequences and Series
Question 3
Important
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Class 11
Important Questions for exams Class 11
- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
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Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability
Transcript
Ex 8.2, 29 If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A ((A+G)(A G)) Let a & b be two numbers We need to show that the numbers are A ((A+G)(A G)) i.e. a = A + (( + )( )) b = A (( + )( )) Now we know that Arithmetic mean =A = ( a+b)/2 Geometric mean =G= ab Putting value of A and G in RHS we can prove it is equal to a and b Solving A (( + )( )) = A ( 2 2) Putting A = ( + )/2 & G = = (( + )/2) ((( + )/2)^2 ( )2) = (( + )/2) ((( + )2 )/4 ) = (( + )/2) (( 2+ 2+2 4 )/4) = (( + )/2) (( 2 + 2 2 )/4) = ( + )/2 (( )2/4) = ( + )/2 ((( )/2)^2 ) = ( + )/2 ( )/2 Thus, A + (( + )( )) = a & A (( + )( )) = b Hence proved.
