Recall the formula for the sum of an infinite geometric series: S=a11−rS=\frac{a_1}{1-r} where a1a_1 is the first element of the series and rr is the common ratio between any two terms (an+1an\frac{a_{n+1}}{a_n} for any nn). This formula only applies for −1<r<1-1<r<1.

For more information, check out Infinite Geometric Series.

Evaluate: ∑k=1∞((78)k+4i3k)\sum_{k=1}^{\infty} \left(\left(\frac{7}{8}\right)^k+\frac{4i}{3^k}\right) where ii is the imaginary number −1\sqrt{-1}.

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