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## anonymous 4 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. 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

2. anonymous

i aint sure but hope that web helps u

3. 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.

4. anonymous

@Hero @experimentX @radar I'd appreciate some help please.

5. experimentX

|dw:1345658958087:dw|

6. experimentX

for value of x=1, try pluggin in WA.

7. 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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