## vf321 Group Title 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? 2 years ago 2 years ago

1. SNSDYoona

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

i aint sure but hope that web helps u

3. vf321

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

5. experimentX

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6. experimentX

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

7. vf321

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.