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# Closed Form for an Infinite Series

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Find a closed form for the infinite series 1+ x + x^2 + x^3 +.... show that the closed form is only valid if /x/< 1, where x may be a complex number (i.e. x=x1 +ix2)

In the complex plane, draw a diagram that shows successive values of 1, 1+x, 1+x+x^2 , 1+x+x^2+x^3, etc. for x=i. Does the series converge for x=i?

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The Closed Form for an Infinite Series is found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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This series is a geometric series and so its infinite sum is 1/(1-x) and this is its closed form.

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