Question

Find the harmonic mean of $\frac{1}{a}$ and $\frac{1}{b}$.

Answer 1

As we know that the harmonic mean of $a,b$ is $\frac{2ab}{a+b}$

So the harmonic mean of $\frac{1}{a},\frac{1}{b}$ is $\frac{2\times \frac{1}{a}\times \frac{1}{b}}{\frac{1}{a}+\frac{1}{b}}=\frac{\frac{2}{ab}}{\frac{a+b}{ab}}=\frac{2}{a+b}$