Computation of a Infinite Sum Using Contour Integration
Not what you're looking for?
Let Cn denote the positively oriented boundary of the square
x = +/- (N + 1/2)pie and y = +/- (N +1/2)pie where N is a positive integer
1) show that
int( dz/ (z^2 sin(z))) = i2pie [ 1/6 + 2sum( (-1)^n / (n^2 pie^2)) n=1]
2) show that sum( (-1)^(n + 1) / n^2 = pie^2 / 12
Purchase this Solution
Solution Summary
In this solution, we show how to compute the infinite sum Sum_{n=1}^infty{(-1)^{n+1}/n^2} by computing an appropriate contour integral.
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.