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?