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

by zetafunction
Tags: divergent, fourier, series, simply, truncate
 P: 399 given a Fourier series of the form $$\sum_{n=0}^{\infty}\frac{cos(nx)}{\sqrt{n}}$$ can i simply truncate this series up to some number finite N so i can get finite results ?? thanks.
 Sci Advisor P: 5,891 You can always truncate the series to get a finite result. However the result as a function of N does not converge to anything.
 Engineering Sci Advisor Thanks P: 6,040 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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