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Math Help - Hard series problem

  1. #1
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    Hard series problem

    Hard series problem-capture.pngProblem in image. I don't know how to start. I can do part b ok. help appreciated thanks
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  2. #2
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    Re: Hard series problem

    Hey GeeRaCeR.

    I don't know what you have covered, but there is a result known as the Euler-Mclaurin formula which links sums, integrals, and error bounds together. Take a look at the wiki in relation to the basel problem (and also note that the basel problem can be written in terms of an integral with a fourier series decomposition):

    Euler?Maclaurin formula - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Hard series problem

    Hi,
    The attachment shows an elementary derivation of the inequality of part a). I leave the other parts to you.

    Hard series problem-mhfcalc39.png
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