Let (an) be a bounded sequence. If 2an <= an+1 + an−1, prove that limit n to infinity of (an+1 − an) = 0. This question is on my exam review sheet for an elementary analysis class and I'm not really sure where to start. Could someone just give me a hint or something? I'm pretty sure an is decreasing and therefore convergent since it's bounded. But I'm not sure how to conclude this or arrive at the final conclusion.