Question

Insert thee harmonic means between $1$ and $7$.

Answer 1

$H.M$ between $1$ &$7$

Let first $3H.M$be $x,x^2,x^3,$

$\Rightarrow x={\left(\frac{7}{1}\right)}^{1/4}=1.6265766$

$x^2=2.6457513$

$x^3=4.3035171$

$x^4=7$ &$x=1$