anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
anonymous
  • anonymous
i aint sure but hope that web helps u
anonymous
  • anonymous
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.

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anonymous
  • anonymous
@Hero @experimentX @radar I'd appreciate some help please.
experimentX
  • experimentX
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experimentX
  • experimentX
for value of x=1, try pluggin in WA.
anonymous
  • anonymous
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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