1. The problem statement, all variables and given/known data I am studying for a calculus test tomorrow on this website (http://archives.math.utk.edu/visual.calculus/6/index.html). I am working on the limit comparison test problems but I am unfamiliar with the form they use in their solutions. For example: Limit comparison test (prove convergence / divergence) Series (from n=1 to ∞) 1/(sqrt(n)+sqrt(n+1)) 2. Relevant equations 3. The attempt at a solution Series (from n=1 to ∞) 1/(sqrt(n)+sqrt(n+1)) compare to Series (from n=1 to ∞) 1/sqrt(n), which we know diverges by the p-series test (p=.5, p<1) Let an = 1/(sqrt(n)+sqrt(n+1)) and bn = 1/sqrt(n) lim(n->∞) an/bn = lim(n->∞) 1/(sqrt(n)+sqrt(n+1)) / 1/sqrt(n) = lim(n->∞) sqrt(n)/(sqrt(n)+sqrt(n+1)) I can see why this limit is 1/2 but I don't understand how the solution to the problem ended up in the form lim(n->∞) 1/(1+sqrt(1-1/n)) = 1/2 I can tell by the other solutions that this form is a rule of sorts but I don't know what it is. Thank you for the help.