Let $a,b,c$ be in AP and $|a|

Question

Let $a,b,c$ be in AP and $|a| < 1,\ |b| < 1,\ |c| < 1$. If $x = 1 + a + a^{2} + ...to\ \infty$, $y = 1 + b + b^{2} + ...to\ \infty$ and $z = 1 + c + c^{2} + ...\infty$, then $x,\ y,\ z$ are in

Dr. Abubacker · Accepted Answer

(c)
Given $x = 1 + a + a^{2} + ...\infty = \frac{1}{1 - a}$
$y = 1 + b + b^{2} + ...\infty = \frac{1}{1 - b}$
and $z = 1 + c + c^{2} + ...\infty = \frac{1}{1 - c}$
Now, a, b, c are in AP.
$\Rightarrow 1 - a,\ 1 - b,\ 1 - c\ are\ in\ AP.$
$\Rightarrow \ \frac{1}{1 - a},\frac{1}{1 - b},\frac{1}{1 - c}$ are in HP.
$\Rightarrow \ x,\ y,\ z\ are\ in\ HP$

Q. Let $a,b,c$ be in AP and $|a| < 1,\ |b| < 1,\ |c| < 1$. If $x = 1 + a + a^{2} + ...to\ \infty$, $y = 1 + b + b^{2} + ...to\ \infty$ and $z = 1 + c + c^{2} + ...\infty$, then $x,\ y,\ z$ are in

Explanation

Reviewed by Dr. Abubacker

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