CalcS5

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Evaluate \sum _{{n=0}}^{\infty }\left({\frac  {i}{3}}\right)^{n}\,.

The series converges because |i/3|=1/3<1\,.

In fact it converges to {\frac  {1}{1-i/3}}={\frac  {3}{4}}+{\frac  {i}{4}}\,.


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