SOLUTION: Evaluate 1 + \frac{i}{3} - \frac{1}{9} - \frac{i}{27} + \frac{1}{81}, where $i$ is the imaginary unit.

Question 1209783: Evaluate
1 + \frac{i}{3} - \frac{1}{9} - \frac{i}{27} + \frac{1}{81},
where $i$ is the imaginary unit.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Combine like terms -- i.e., combine the real terms and combine the imaginary terms.

ANSWER: (73/81)+(8/27)i

It is possible that the sequence was supposed to be an infinite sequence instead of a finite one. In that case....

Sum = (first term)/(1-common difference)

ANSWER: (9+3i)/10

Alternatively, we can find the infinite sums of the real and imaginary parts separately.

Real parts: first term 1, common ratio (-1/9)

Sum =

Imaginary parts: first term i/3, common ratio (-1/9)

ANSWER: (9/10)+(3/10)i

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