Let a,b,c |a|<1,|b|<1,|c|<1, if x=1+a+a2+⋯to ∞ y=1+b+b2+⋯ to ∞z=1+c+c2+⋯ to ∞ then x,y,z are in

x=1+a+a2+⋯|a|<1x=11−ay=1+b+b2+⋯|b|<1y=11−bz=1+c+c2+⋯|c|<1z=11−ca,b,c→A.P1−a,1−b,1−c→A.P11−a,11−b,11−c→H.Px,y,z→H.P

Let a,b,c |a|<1,|b|<1,|c|<1, if x=1+a+a2+⋯to ∞ y=1+b+b2+⋯ to ∞z=1+c+c2+⋯ to ∞ then x,y,z are in

x=1+a+a2+⋯|a|<1x=11−ay=1+b+b2+⋯|b|<1y=11−bz=1+c+c2+⋯|c|<1z=11−ca,b,c→A.P1−a,1−b,1−c→A.P11−a,11−b,11−c→H.Px,y,z→H.P

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Let $a, b, c$ $| a | < 1, | b | < 1, | c | < 1$ , if $x = 1 + a + a^{2} + \dots to \infty$ $y = 1 + b + b^{2} + \dots to \infty$ $z = 1 + c + c^{2} + \dots to \infty then x, y, z are in$

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Detailed Solution

$\begin{array}{l} x = 1 + a + a^{2} + \dots | a | < 1 \\ x = \frac{1}{1 - a} \\ y = 1 + b + b^{2} + \dots | b | < 1 \\ y = \frac{1}{1 - b} \\ z = 1 + c + c^{2} + \dots | c | < 1 \\ z = \frac{1}{1 - c} \\ a, b, c \to A . P \\ 1 - a, 1 - b, 1 - c \to A . P \\ \frac{1}{1 - a}, \frac{1}{1 - b}, \frac{1}{1 - c} \to H . P \\ x, y, z \to H . P \end{array}$