# Fourier series understanding problem

## Homework Statement

So the question is how does

4/π*(sin(πx))+4/3π *(sin(3πx))+4/5π *(sin(5πx)) = 1

for values of 0<x<1

## Homework Equations

No relevant equation needed just don't understand which values of x to take.

## The Attempt at a Solution

I am not sure which value of x to start with, it could be anything 0.1 or 0.5, how do I know which x value to start with? I have taken 0.5 and ended up with 1.05 and then taken 0.9 and ended up with 1.15. How the hell does this equal to 1 for any x value?!!!! Please help...

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Chestermiller
Mentor

## Homework Statement

So the question is how does

4/π*(sin(πx))+4/3π *(sin(3πx))+4/5π *(sin(5πx)) = 1

for values of 0<x<1

## Homework Equations

No relevant equation needed just don't understand which values of x to take.

## The Attempt at a Solution

I am not sure which value of x to start with, it could be anything 0.1 or 0.5, how do I know which x value to start with? I have taken 0.5 and ended up with 1.05 and then taken 0.9 and ended up with 1.15. How the hell does this equal to 1 for any x value?!!!! Please help...
You're missing some terms in the series, starting with the sin(7πx) term. Was there a sequence of 3 dots ... in the equation you were given? The three dots indicate an infinite series.

Chet

Yeah there were few other terms, the consecutive odd n's, I just didn't write it, sorry! and also yeah sequence of 3 dots so its infinity....but I still don't get it...can you explain how it equals 1...

Chestermiller
Mentor
Yeah there were few other terms, the consecutive odd n's, I just didn't write it, sorry! and also yeah sequence of 3 dots so its infinity....but I still don't get it...can you explain how it equals 1...
Are you familiar with half-wave Fourier series? Or, can you expand the following function in a Fourier series:

y = -1 from x = -1 to x = 0

y = +1 from x = 0 to x = +1

Also, in terms of the series you have written, just try including more terms in the summation (say, up to 20) and see what you get when you evaluate the value at x = 0.5.

Chet

Last edited:
Are you familiar with half-wave Fourier series? Or, can you expand the following function in a Fourier series:

y = -1 from x = -1 to x = 0

y = +1 from x = 0 to x = +1

Also, in terms of the series you have written, just try including more terms in the summation (say, up to 20) and see what you get when you evaluate the value at x = 0.5.

Chet
No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!

Chestermiller
Mentor
No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!
I can't know what they ask you to do on your exams.

If the question is, "how well does the three term expression you wrote match y = 1 over the interval 0<x<1?", just plot a graph of the expression as a function of x. Evaluate x every 0.05 over the interval. You can use a spreadsheet to do this type of calculation easily. Then plot the graph. I think you will be surprised at how well it fits over the entire interval with only three terms.

Chet

LCKurtz
Homework Helper
Gold Member
No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!
More likely they are wanting you to know some of the theory about how a FS represents a function. Have you heard of the Dirichlet conditions? Do you know what the FS does when there is a jump discontinuity in the function? You don't have to literally add the series to know what the sum looks like.

Nope I don't....but you could always tell me....

LCKurtz