Recent content by lainyg

Another: Let {q(n)n} and {p(n)} (for all integer n's) be Cauchy Sequences which are equivalent. Further let {a(n)} and {b(n)} also be Cauchy Sequences which are equivalent. Show {q(n) * a(n)} = {p(n) * b(n)} (for all integer n's)

OK, so.. if qn converges, then for any epsilon>0 there exists a natural N such that (qn when N=k) is less than epsilon. With the maclaurin formula we can write that e^x = the sum (from n=0 to infinity) of x^n/n!. Therefore can we just say that since the lim (as n approaches infinity) of...

Homework Statement q(n) = Sum(from k=1 to n) 1/n! Exercise 3: Prove that {q(n)}n(forall)Ns is a cauchy sequence. Homework Equations none. The Attempt at a Solution So many attempts at a solution. I know that a sequence is a cauchy sequence if for all epsilons greater than...