1. The problem statement, all variables and given/known data Let an be a bounded sequence and bn such that the limit bn as n→∞ is b and 0<bn ≤ 1/2 (bn-1) Prove that if: an+1 ≥ an - bn, then lim an n→∞ exists. 2. Relevant equations 3. The attempt at a solution as 0<bn ≤ 1/2 (bn-1) the sequence bn is decreasing. thus its limit, b, is 0 (can i assume that?) Then, assuming an converges to a limit, say p, the equation is: p ≥ p - b where b=0 p ≥ p is true for every p. Then, an is constant and therefore converges. Does is it work like that?