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

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(B) Given the infinite geometric series: $A = 1 + r^z + r^{2z} + r^{3z} + .......\infty$.This is a geometric progression with the first term $a = 1$ a

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

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(B) Given the infinite geometric series: $A = 1 + r^z + r^{2z} + r^{3z} + .......\infty$.This is a geometric progression with the first term $a = 1$ and common ratio $R = r^z$.The sum of an infinite geometric series is given by $S_{\infty} = \frac{a}{1 - R}$,provided $|R| Substituting the values,we get $A = \frac{1}{1 - r^z}$.Rearranging the equation to solve for $r^z$:$1 - r^z = \frac{1}{A}$$r^z = 1 - \frac{1}{A}$$r^z = \frac{A - 1}{A}$Taking the $z$-th root on both sides,we get $r = \left( \frac{A - 1}{A} \right)^{1/z}$.

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

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