To find the sum of a fourier series ?

In summary, the conversation is about finding the sum of a Fourier series, specifically ((-1)^(n+1))/2n-1 from n=1 to infinity. The person is unsure about how to approach the problem and is asking for help. There is a suggestion to use the series for log(1+x) with x=i, but it is noted that this is not technically a Fourier series.
  • #1
cabellos
77
1
to find the sum of a Fourier series...?

My problem is:

I must find the sum of ((-1)^(n+1))/2n-1 between infinity and n=1.

I have looked in all my available textbooks for a clear example but I am still unsure as to how i should approach the problem?

Help with this would be much appreciated.

Thankyou.
 
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  • #2
Do you really have to sum it, or just show it converges? The former is easy. I'm not sure how to do the latter unless someone can think of a taylor series that resembles your series.
 
  • #3
Try this. Take the series for log(1+x) and think about putting x=i.
 
  • #4
But that's not a "Fourier series", that's just a power series.
 

What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as a sum of sinusoidal functions. It is used to analyze and approximate a wide range of periodic and non-periodic functions.

What is the formula for finding the sum of a Fourier series?

The formula for finding the sum of a Fourier series is given by:
f(x) = a0/2 + ∑[ancos(nω0x) + bnsin(nω0x)]
where an and bn are the Fourier coefficients and ω0 is the fundamental frequency.

What are the applications of Fourier series?

Fourier series have a wide range of applications in various fields such as engineering, physics, signal processing, and mathematics. They are used to analyze and approximate periodic functions, solve differential equations, and understand the behavior of complex systems.

How do you determine the coefficients for a Fourier series?

The coefficients for a Fourier series can be determined by using the Fourier series formula and solving for the values of an and bn. This is usually done by using integration techniques and manipulating the given function.

What are the limitations of using a Fourier series?

Although Fourier series are a powerful tool for approximating functions, they have some limitations. They can only be used for functions that are periodic, and they may not converge for some functions with discontinuities or sharp corners. Additionally, the accuracy of the approximation depends on the number of terms used in the series.

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