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Q.

If the harmonic mean of $\frac{1}{a}$ and $\frac{1}{b}$ is

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a

\frac{a + b}{2 a b}

b

\frac{2}{a + b}

c

\frac{a + b}{2}

d

\frac{a - b}{2}

answer is C.

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Detailed Solution

\frac{1}{a}

and

\frac{1}{b}

$H . M$ of $\frac{1}{a}$ and $\frac{1}{b}$

$= \frac{2 (\frac{1}{a}) (\frac{1}{b})}{\frac{1}{a} + \frac{1}{b}}$

$= \frac{\frac{2}{a b}}{\frac{a + b}{a b}}$

$= \frac{2}{a + b}$

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If the harmonic mean of 1a and 1b is