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vf321

  • 3 years ago

Can a real-valued function f(x, k) which has domain x: Reals and k: Positive integers and 0 have the following property?\[\lim_{n\rightarrow\infty}\sum_{k=0}^n\int f(x,k)dx\]The above converges for some x while the below diverges\[\lim_{n\rightarrow\infty}\sum_{k=0}^nf(x,k)\]for the same x?

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  1. SNSDYoona
    • 3 years ago
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    haha i think u shud try this website.. its pretty helpful on those sequences and series http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

  2. SNSDYoona
    • 3 years ago
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    i aint sure but hope that web helps u

  3. vf321
    • 3 years ago
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    I appreciate your try to help but I did pass calculus and if it could have been solved that easily then I wouldn't have asked.

  4. vf321
    • 3 years ago
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    @Hero @experimentX @radar I'd appreciate some help please.

  5. experimentX
    • 3 years ago
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    |dw:1345658958087:dw|

  6. experimentX
    • 3 years ago
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    for value of x=1, try pluggin in WA.

  7. vf321
    • 3 years ago
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    Interesting. So we get: \[\sum_{k=0}^\infty\frac{x^{k^2+1}}{k^2+1}\] Which does indeed converge for x = 1 by p-series and direct comparison test.

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