Convergence of a Series with Trig Functions

HypeBeast23
Messages
4
Reaction score
0

Homework Statement



*The sum from n = 1 to infinity* (cos(n*pi))^2/n*pi where n is the variable.

Homework Equations



All forms of convergence tests (i.e. Ratio Test, Integral Test, Alternating Series test etc.)

The Attempt at a Solution



I am having trouble figuring out which route to take to tackle this question. Any help would be appreciated!
 
Physics news on Phys.org
Try writing out the first few terms of the series. You'll see it's not as complicated as you think.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

How to show that these sequences are summable?
Replies
1
Views
1K
Ratio Test vs AST
Replies
4
Views
1K
On pointwise convergence of Fourier series
Replies
3
Views
2K
Intervals of Convergence- Power Series
Replies
11
Views
3K
Power Series and Convergence for ln(x+1)
Replies
22
Views
4K
Finding the r value for the series to converge
Replies
15
Views
2K
Interval of uniform convergence of a series
Replies
24
Views
3K
Prove that this series converges uniformly on R
Replies
4
Views
1K
Using the Integral Test to Show Sum is Less Than pi/2
Replies
13
Views
2K
Proving the convergence of series
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top