it's a fact that every convergent sequence is bounded. recall that, by definition, a sequence {An}has the limit L if for every W>0 there is a corresponding integer N such that

absolute value of (An-L)<W whereever n>N

Use this definition to prove that every sequence that converges to 0 is bounded, i.e to prove that if lim(n is infinity) An =0 then there is a positive number M such that absolute value of (An)<= M for all n belong to natural numbers.