can we simply truncate a Fourier series if it is divergent??

zetafunction

given a Fourier series of the form

[tex] \sum_{n=0}^{\infty}\frac{cos(nx)}{\sqrt{n}}[/tex]

can i simply truncate this series up to some number finite N so i can get finite results ?? thanks.

mathman

You can always truncate the series to get a finite result. However the result as a function of N does not converge to anything.

AlephZero

Maybe a more fundamental question is "what is your series supposed to represent?" For eaxmple, the energy (measured as the function squared) is ##\sum (1/n)## which is infinite.

As mathman said, you can do anything you like mathematically with a finite number of terms, but whether the result means anything is another question.

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zetafunction	can we simply truncate a Fourier series if it is divergent?? Tweet given a Fourier series of the form [tex] \sum_{n=0}^{\infty}\frac{cos(nx)}{\sqrt{n}}[/tex] can i simply truncate this series up to some number finite N so i can get finite results ?? thanks.

mathman Recognitions: Science Advisor	You can always truncate the series to get a finite result. However the result as a function of N does not converge to anything.

AlephZero $Math 2012$ Recognitions: Science Advisor	Maybe a more fundamental question is "what is your series supposed to represent?" For eaxmple, the energy (measured as the function squared) is ##\sum (1/n)## which is infinite. As mathman said, you can do anything you like mathematically with a finite number of terms, but whether the result means anything is another question.