Harmonic Mean

If two harmonic means between $7$ and $8$ are $\frac{168}{23}$and $\frac{168}{22}$ then find single harmonic mean between these two numbers.

If two harmonic means between $5$ and $11$ are $\frac{55}{9}$and $\frac{55}{7}$ then the single harmonic mean between these two numbers$=$$\frac{55}{m}$, find $m$.

Three harmonic means between $1$ and $5$ are $\frac{5}{4}, \frac{5}{3}$ and _____.

Insert two harmonic means between $7 \text{and} 8$.

Find the relation among single harmonic mean and $3$ harmonic means between $\frac{1}{12} \text{and} \frac{1}{20}$.

If four harmonic means between $\frac{1}{2} \text{and} \frac{1}{22}$ are $\frac{1}{6},\frac{1}{10},\frac{1}{14},\frac{1}{18}$ then find single harmonic mean between these two numbers.

Find the sum of reciprocal of two harmonic means between $7 \text{and} 8$.

Insert three harmonic means between $2 \text{and} 3$.

Insert three harmonic means between $1 \text{and} \frac{1}{9}$.

Let the harmonic mean and geometric mean of two positive number be in the ratio $4: 5$. then the ratio of two number is $\lambda (\lambda <1),$ find $11\lambda$. 

If $2\left(y – a\right)$ is the $\mathrm{H}.\mathrm{M}.$ between $y – x$ and $y – z$, then $x-a,\mathrm{ }\mathrm{ }y-a,\mathrm{ }\mathrm{ }z-a$ are in

The harmonic mean between two numbers is $14\frac{2}{5}$ and the geometric mean is $24$. The greater number between them is

If $\mathrm{G}.\mathrm{M}.$ and $\mathrm{H}.\mathrm{M}.$ of two numbers are $10$ and $8$ respectively. The numbers are

If $H$ is the harmonic mean between $p$ and $q$, then the value of $\frac{H}{p}+\frac{H}{q}$ is

$\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the $\mathrm{A}.\mathrm{M}.$ of $a$ and $b,$ if $n=$

If $a_i>0, i=1, 2, 3,...,50$ and $a_1+a_2+a_3+...+a_{50}=50$, then the minimum value of $\frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}+...+\frac{1}{a_{50}}$  is equal to.

The harmonic mean of the roots of the equation.
$\left(5+\sqrt{2}\right)x^2-\left(4+\sqrt{5}\right)x+8+2\sqrt{5}=\mathrm{0\; is}$