x^n/n! = 0 for n-> 0

using sandwich theorem

a sequence given by a(n+1) = SQRT(2 + an)

prove that it is converging.. I found the limit is 2.. but how to prove it converges?

prove that if an converges to a and bn converges to b then an/bn converges to a/b using the theorem |an-l| < E for all n > N and for any E > 0