A sequence (Sn) is said to be contractive if there exists k with 0<k<1 such that |S(n+2) - S(n+1)| <= k|S(n+1) - Sn| for all n is an element of N. Prove that every contractive sequence is a Cauchy sequence, and hence is convergent
A sequence (Sn) is said to be contractive if there exists k with 0<k<1 such that |S(n+2) - S(n+1)| <= k|S(n+1) - Sn| for all n is an element of N. Prove that every contractive sequence is a Cauchy sequence, and hence is convergent