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STD 11 - 8. sequence and series — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 8. sequence and series1 Mark
MCQ
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
  • A
    $x, y, z$ are in $A.P.$
  • ✓
    $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in $A.P.$
  • C
    $x, y, z$ are in $G.P.$
  • D
    $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1-(a+b+c)$
✓

Answer

Correct option: B.
$\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in $A.P.$
b
$x =1+ a + a ^{2}=\ldots \ldots \ldots .$

$x=\frac{1}{1-a} \Rightarrow a=1-\frac{1}{x}$

$y=\frac{1}{1-b} \Rightarrow b=1-\frac{1}{y}$

$z=\frac{1}{1-c} \Rightarrow c=1-\frac{1}{z}$

$a , b , c$ are in $A.P.$

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

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

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

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