Question

If $r>1$ and $x=a+\frac{a}{r}+\frac{a}{r^2}+$_____ to $\infty$ $y=b-\frac{b}{r}+\frac{b}{r^2}-$_____ to $\infty$ and $z=c+\frac{c}{r^2}+\frac{c}{r^4}+$_____ to $\infty$, then $\frac{xy}{z}=$

• A. $\frac{ab}{c}$
• B. $\frac{ac}{b}$
• C. $\frac{bc}{a}$
• D. None of these

Answer 1

The correct option is A $\frac{ab}{c}$

Let, $r>1$ and $x=a+\frac{a}{r}+\frac{a}{r^2}+$_____ to $\infty =\frac{a}{1-\frac{1}{r}}=\frac{ar}{r-1}$........(1).

$y=b-\frac{b}{r}+\frac{b}{r^2}-$_____ to $\infty =\frac{b}{1+\frac{1}{r}}=\frac{br}{r+1}$.......(2).

and $z=c+\frac{c}{r^2}+\frac{c}{r^4}+$_____ to $\infty =\frac{c}{1-\frac{1}{r^2}}=\frac{c{r}^2}{r^2-1}$........(3).

Now

$\frac{xy}{z}$

$=\frac{\frac{ab{r}^2}{r^2-1}}{\frac{c{r}^2}{r^2-1}}$

$=\frac{ab}{c}$ [Using (1).(2) and (3)]