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 2 years ago
Can a realvalued 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
Can a realvalued 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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SNSDYoona
 2 years ago
Best ResponseYou've already chosen the best response.0haha i think u shud try this website.. its pretty helpful on those sequences and series http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

SNSDYoona
 2 years ago
Best ResponseYou've already chosen the best response.0i aint sure but hope that web helps u

vf321
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.

vf321
 2 years ago
Best ResponseYou've already chosen the best response.0@Hero @experimentX @radar I'd appreciate some help please.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1345658958087:dw

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1for value of x=1, try pluggin in WA.

vf321
 2 years ago
Best ResponseYou've already chosen the best response.0Interesting. So we get: \[\sum_{k=0}^\infty\frac{x^{k^2+1}}{k^2+1}\] Which does indeed converge for x = 1 by pseries and direct comparison test.
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