If A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .... | vedclass

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(b) $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + ........\infty $

$A = 1 + [{r^z} + {r^{2z}} + {r^{3z}} + ........\infty ]$

We know that sum of infini

Vedclass · Accepted Answer

${\left( {\frac{{A - 1}}{A}} \right)^{1/z}}$

Vedclass · Answer

(b) $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + ........\infty $

$A = 1 + [{r^z} + {r^{2z}} + {r^{3z}} + ........\infty ]$

We know that sum of infinite $G.P.$ is

${S_\infty } = \frac{a}{{1 - r}}( - 1 < r < 1)$

Therefore, $A = 1 + \left[ {\frac{{{r^z}}}{{1 - {r^z}}}} ight]$

$\Rightarrow A = \frac{{1 - {r^z} + {r^z}}}{{1 - {r^z}}}$

$	herefore $ $A = \frac{1}{{1 - {r^z}}}$

$\Rightarrow 1 - {r^z} = \frac{1}{A} $

$\Rightarrow {r^z} = \frac{{A - 1}}{A}$

Hence $r = {\left[ {\frac{{A - 1}}{A}} ight]^{1/z}}$.

If $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .......\infty $, then the value of $r$ will be

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