According to Hardy's book "divergent series" the sum:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] g(x)=1/2+cos(x)+cos(2x)+cos(3x)+....... [/tex] has sum equal to 0 (¡¡¡¡¡¡) then if we integrate in the sense:

[tex] \int_{0}^{b}f(x)\sum_{n=0}^{\infty}cos(nx) dx \rightarrow (-1/2)\int_{0}^{b}f(x)dx [/tex] since the sum "regularized" has the value 0..but is this true?...can you manipulate divergent series giving them a "sum" although they diverge and even in this case that is clearly 0?..

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# Strange resummation

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