If $x=\sum \limits_{n=0}^{\infty} a^{n}, y=\sum\limits_{n=0}^{\infty} b^{n}, z=\sum\limits_{n=0}^{\infty} c^{n}$, where $a , b , c$ are in $A.P.$ and $|a| < 1,|b| < 1,|c| < 1$, $abc \neq 0$, then

  • [JEE MAIN 2022]
  • A

    $x, y, z$ are in $A.P.$

  • B

    $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in $A.P.$

  • C

    $x, y, z$ are in $G.P.$

  • D

    $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1-(a+b+c)$

Similar Questions

The value of $\sum\limits_{r = 1}^n {\log \left( {\frac{{{a^r}}}{{{b^{r - 1}}}}} \right)} $ is

If three numbers be in $G.P.$, then their logarithms will be in

If the sides of a right angled traingle are in $A.P.$, then the sides are proportional to

If $a,\;b,\;c$ are in $A.P.$, then $\frac{{{{(a - c)}^2}}}{{({b^2} - ac)}} = $

If $(b+c),(c+a),(a+b)$ are in $H.P$ , then $a^2,b^2,c^2$ are in.......