The value of $\sum_{n=0}^{\infty}\left(\frac{2 i}{3}\right)^n$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \sum_{n=0}^x\left(\frac{2 i}{3}ight)^n \ &=1+\left(\frac{2 i}{3}ight)+\left(\frac{2 i}{3}ight)^2+\left(\frac{2 i}{3}ight)^3+\ldots . \ &=\frac{1}{1-\frac{2 i}{3}}=\frac{3}{3-2 i} 	imes \frac{3+2 i}{3+2 i}\end{aligned}$

The value of $\sum_{n=0}^{\infty}\left(\frac{2 i}{3}\right)^n$ is

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