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