Let  be a nondecreasing sequence, which is bounded above, and let L be the least upper bou...

Let  be a nondecreasing sequence, which is bounded above, and let L be the least upper bound of the set {an| n = 1,2,...}. Prove that for every real number Ɛ > 0, there exists a positive integer N such that L - Ɛ < an<L  for every n > N. In calculus terminology, a nondecreasing sequence, which is bounded above, Converges to the limit L,  where L is the least upper bound of the set of elements of the sequence.