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I have a sum which is normal convergent and I know the limit-function of the sum, does it implies that the sum of the absolute values of each term converges to the absolute value of the function?

guest
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  • the sum is a Fourier series and by the theorem of Dirichlet I know it converges normally to a certain function, but Im looking for the value of the sum of the absolute term of this series – guest Apr 05 '16 at 14:43
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    It has absolutely no reason to converge to the absolute value of the sum, since $\lvert x+y\rvert\neq\lvert x\rvert+\lvert y\rvert$ in general. – Bernard Apr 05 '16 at 14:48
  • I understand, so im still stuck. – guest Apr 05 '16 at 14:51

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