Let a(n) and b(n) be convergent sequences of real numbers such that the limit of a(n) as n approaches infinity is A and the limit of b(n) as n approaches infinity is B for some real numbers A and B. Show (using the epsilon-N definition of a limit) that

(a) the limit of a(n) + b(n) as n approaches infinity = A + B

(b) the limit of a(n)b(n) as n approaches infinity = AB