Test for convergence or divergence
1.) sum from n=1 to infinity of (e^1/n)/(n^2)
2.) sum from j=1 to infinity of (-1)^j * ((sqrt j)/(j+5))
3.) sum from n=2 to infinity of (1/((1+n)^(ln n))
Series are tested for convergence. The solution is detailed and well presented.