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

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Question

(b) $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + ........\infty $

$A = 1 + [{r^z} + {r^{2z}} + {r^{3z}} + ........\infty ]$

हम जानते हैं, गुणोत्तर श्र

Vedclass · Accepted Answer

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

Vedclass · Answer

(b) $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + ........\infty $

$A = 1 + [{r^z} + {r^{2z}} + {r^{3z}} + ........\infty ]$

हम जानते हैं, गुणोत्तर श्रेणी के अनन्त पदों का योगफल

${S_\infty } = \frac{a}{{1 - r}}$,  $( - 1 < r < 1)$

अत:, $A = 1 + \left[ {\frac{{{r^z}}}{{1 - {r^z}}}} ight]$

$\Rightarrow A = \frac{{1 - {r^z} + {r^z}}}{{1 - {r^z}}}$

$	herefore $ $A = \frac{1}{{1 - {r^z}}}$

$\Rightarrow 1 - {r^z} =\frac{1}{A}$

$\Rightarrow {r^z} = \frac{{A - 1}}{A}$

अत: $r = {\left[ {\frac{{A - 1}}{A}} ight]^{1/z}}$.

यदि $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .......\infty $, तो $r$ का मान होगा

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