(adsbygoogle = window.adsbygoogle || []).push({}); Finding if a series is convergent-Answered

1. The problem statement, all variables and given/known data

Find for which values of K is the fallowing series convergent.

[tex]\sum[/tex]((n!)^{2})/((kn)!)

where:

N is the variable.

K is a constant or a list of constant (eg. "(2,91]")

2. Relevant equations

I believe the ratio test, which states that if (f(n+1)/(f(n) as n approaches infinity is less then 1, it converges.

3. The attempt at a solution

I believe the obvious way to go about this would be the ratio test which is as fallows"

[PLAIN]http://img688.imageshack.us/img688/2140/equation1.png [Broken]

[PLAIN]http://img146.imageshack.us/img146/2783/equation2.png [Broken]

[PLAIN]http://img232.imageshack.us/img232/1554/equation3.png [Broken]

1>((n+1)!*(n+1)!/(k(n+1))!*((Kn)!/(n!*n!) as n[tex]\rightarrow[/tex] [tex]\infty[/tex]

1>(n+1)(n+1)/(k(n+1)) as n[tex]\rightarrow[/tex] [tex]\infty[/tex]

1> (n+1)/k

which is not true, therefore this series must diverge for any possible K.

my question: am i doing anything wrong or did the teacher give a trick question?

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# Homework Help: Finding if a series is convergent.

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