1/ln((n)!) [n goes from 2-infinity] 1/ln((2)!) + 1/ln((3)!) +1 /ln((4)!) +......+ 1/ln((n)!) the first thing i thought of was de lambert lim An+1/An n->inf =ln(x!)/ln((x+1)!) =ln(x!)/ln(x!*(x+1)) =ln(x!)/[ln(x!)+ln(x+1)] =1-ln(x+1)/[ln(x!)+ln(x+1)]=1 which doesnt tell me anything about the convergence /divegence of the series. have i done something wrong somewhere here, or is there another way to solve this?