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

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(B) Given the infinite geometric series: $A = 1 + r^z + r^{2z} + r^{3z} + \dots \infty$This can be written as: $A = 1 + [r^z + r^{2z} + r^{3z} + \dots

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

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(B) Given the infinite geometric series: $A = 1 + r^z + r^{2z} + r^{3z} + \dots \infty$This can be written as: $A = 1 + [r^z + r^{2z} + r^{3z} + \dots \infty]$The sum of an infinite geometric progression is given by $S_{\infty} = \frac{a}{1 - r_{ratio}}$,where $|r_{ratio}| Substituting this into the equation:$A = 1 + \frac{r^z}{1 - r^z}$Simplify the expression:$A = \frac{1 - r^z + r^z}{1 - r^z}$$A = \frac{1}{1 - r^z}$Rearranging to solve for $r^z$:$1 - r^z = \frac{1}{A}$$r^z = 1 - \frac{1}{A}$$r^z = \frac{A - 1}{A}$Taking the $z$-th root on both sides:$r = \left( \frac{A - 1}{A} \right)^{1/z}$

If $A = 1 + r^z + r^{2z} + r^{3z} + \dots \infty$,then the value of $r$ is:

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