I'm trying to find out under which conditions does a

Potherat8mi

Potherat8mi

Answered question

2022-02-18

I'm trying to find out under which conditions does a sum of a rational function f(n) converges, with f(x)=A(x)B(x), with degB>degA and X,B(X)0.
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Answer & Explanation

Haiden Frazier

Haiden Frazier

Beginner2022-02-19Added 10 answers

As long as convergence is concerned, assume that we're summing n=Nf(n) where N is large enough so that B(n)0 for nN and f(n) is always well-defined.
If f(n)0 for large n then consider -f(n) instead. We have f(n)CndegAndegB=C.1ndegBndegA so that by comparison this series is convergent precisely when degB=degA>1, that is degBdegA+2.

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