I have this proof class that is really bugging me with problems like these, I'd appreciate if someone could help me please.

(a) Let (Sn) be a sequence such that |Sn+1 - Sn|<2^-n for all n inNProve that (Sn) is a Cauchy sequence and hence a convergent sequence.

(b) Is the result in (a) true if we only assume that |Sn+1 - Sn|<1/n for all n inN?