1. The problem statement, all variables and given/known data Evaluate lim sqrt(n)*[sqrt(n+1)-sqrt(n)] 2. Relevant equations sqrt(n)/[sqrt(n+1)+sqrt(n)] = 1/sqrt[1+(1/n)]+1 3. The attempt at a solution I know that limit sqrt(n) = Infinity and that limit (sqrt(n+1)-sqrt(n)) = 0. And I know that sqrt(n)*(sqrt(n+1)-sqrt(n)) = sqrt(n)/(sqrt(n+1)+sqrt(n)). I believe the limit of the product of these sequences is 1/2, but I am not sure how to get there. I need to do an epsilon proof of the limit and I am not sure how to solve the equation in 2. in terms of epsilon. Thanks for your help.