Question 11, Exercise 4.6

Solutions of Question 11 of Exercise 4.6 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Find H.M. between $\dfrac{2}{3}$ and $\dfrac{4}{7}$.

Solution.

Here $a=\dfrac{2}{3}$ and $b=\dfrac{4}{7}$, therefore

$$\begin{align*} \text{H.M.}&=\frac{2ab}{a+b} \\ &=\frac{2\times\frac{2}{3}\times\frac{4}{7}}{\frac{2}{3}+\frac{4}{7}} \\ &=\frac{16/21}{26/21} \\ &=\frac{8}{13} \\ \end{align*}$$ Hence $\dfrac{8}{13}$ is H.M between $\dfrac{2}{3}$ and $\dfrac{4}{7}$.

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