Purchase Solution

Closed Form for an Infinite Series

Not what you're looking for?

Ask Custom Question

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?

Purchase this Solution

Solution Summary

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.

Solution Preview

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

The ...

Purchase this Solution

Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.