$\,8(i)\,$ If $\,y\,$ is the H.M. between $\,x\,$ and $\,z\,$, prove that  $\,\frac{1}{y-x}+\frac{1}{y-z}=\frac 1x+\f…

$\,5.\,$ If $\,a,b,c\,$ are in H.P., prove that $\,(i)\,~~\frac{a}{b+c-a},\frac{b}{c+a-b},\frac{c}{a+b-c}\,$ are in H…

$\,3(i).\,$ What is the value of the H.M. between $\,(a+b)\,$ and $\,(a-b)?$ Sol. Let $\,m\,$ be the the H.M. between…

$\,1.\,$ Examine whether the following sequences are in H.P. $\,(i)\,\,\{\frac 35,\frac{3}{11},\frac{3}{17},\frac{3}{…