Question

$\frac{1}{a},\frac{1}{b}$ and $\frac{1}{c}$ are in A.P. Show that: bc, ca and ab are also in A.P.

Answer 1

$\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P

$\frac{2}{b}=\frac{1}{a}+\frac{1}{c}\frac{2}{b}=\frac{a+c}{ac}2ac=ab+bc$

$ab,ac,bc$ are in A.P

(or) $bc,ac,ab$ are in A.P