1. The problem statement, all variables and given/known data Hey, so here is the problem: Suppose 0≤c<1 and let an = (1 + c)(1 + c2)...(1 + cn) for integer n≥1. Show that this sequence is convergent. Well I understand the basic concepts of proving convergence of sequences, but in class we've only ever done it with sequences where the terms are summed not multiplied like this one is. I guess I'm just having trouble figuring out where to go really... 2. Relevant equations I guessed we either need to use the theorem that says any bounded monotone sequence is convergent. Or by simply finding the limit L and proving that the sequence converges to L. 3. The attempt at a solution There's a suggestion that says " Show that 1 + c ≤ ec ". I did that by showing that if c = 0, then 1 + 0 = e0 = 1 And then for any c>0 d/dc(1 + c) < d/dc(ec). Therefore for any c≥0, 1 + c ≤ ec. Now I don't really know how to use this to solve my problem. I tried to show that the sequence is monotone: As an+1 = an(1+cn+1) Therefore an+1 ≥ an Therefore an is non-decreasing, therefore monotone. But now I have no idea what to do. I really need help cause my prof just says that it should be obvious.