I have two questions one is just about part of the problem and the other one I want to make sure I am going in the right direction. The directions are "For each of the following series, determine whether it converges, converges absolutely, or diverges" 1) [tex]\sum[/tex](n^n)/(n!n!) here I can use ratio test [(n+1)^(n+1)/[(n+1)!(n+1)!]]/[n^n/(n!n!)] [[(n+1)^(n+1)]*(n!n!)]/[n^n*[(n+1)!(n+1)!]] [(n+1)(n+1)^n(n!)(n!)]/[(n+1)n!(n+1)n!(n^n)] (n+1)^n/[(n+1)n^n] and here is my problem I know that we can write (n+1)! as (n+1)n! and (n+1)^n as n but then what is (n+1) and n^n. 2) [tex]\sum[/tex](n^2+1)^(1/2)-1 in order to figure out if it converges/diverges could I use the comparison test where: [(n^2+1)^(1/2)-1]/(n^(2/2) [(1+(1/n))^(1/2)-1] so 1^(1/2) is 1 hence in converges If this is not the way to do it am I at least using the correct test? Thank you in advance.