આપણી પાસે ${\text{a}}\,\, = \,\,\sum\limits_{{\text{n}}\, = \,{\text{0}}}^\infty {{{\text{x}}^{\text{n}}}} \,\, = \,\,\frac{1}{{1\,\, - \,\,x}}$ $\,\, \Rightarrow \,\,x\,\, = \,\,\frac{{a\,\, - \,\,1}}{a}$ છે.
$b\,\, = \,\,\sum\limits_{n\, = \,0}^\infty {{y^n}} \, = \,\,\frac{1}{{1\,\, - \,\,y}}$
$ \Rightarrow \,\,y\,\, = \,\,\frac{{b\,\, - \,\,1}}{a}$
$c\,\, = \,\,\sum\limits_{n\, = \,0}^\infty {{{(xy)}^n}} $
$ \Rightarrow \,\,\frac{1}{{1\,\, - \,\,xy}}\,\,\, \Rightarrow \,\,xy\,\, = \,\,\frac{{c\,\, - \,\,1}}{c}$
$\therefore \,\,\frac{{a\,\, - \,\,1}}{a}\,\,.\,\,\frac{{b\,\, - \,\,1}}{b}\,\, = \,\,\frac{{c\,\, - \,\,1}}{c}$
$ \Rightarrow \,\,ab\,\, + \,\,c\,\, = \,\,ac\,\, + \,\,bc$