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BITSAT2021MathematicsSequences and SeriesActual

If the harmonic mean between a and b be H , then the value of 1 H -a + 1 H -b is

Options

  1. Aa+b
  2. Ba b
  3. C1 a + 1 b
  4. D1 a - 1 b

Correct answer

C. 1 a + 1 b

Step-by-step solution

Putting H = 2 a b a+b , we have array l 1 H -a + 1 H -b = 1 ( 2 a b a+b -a ) + 1 ( 2 a b a+b -b ) = a+b a b-a² + a+b a b-b² array = ( a+b b-a ) ( 1 a - 1 b )= ( a+b b-a ) ( b-a a b )= a+b a b = 1 a + 1 b

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