Hello all,
I have the following sequence: where . The objective is to prove that it is bounded above and below. Also, we need to prove that it has no smallest element. I succeeded in proving that it is bounded below: (let with and continue from there). For the other questions, I think it would be enough if we can prove that the sequence is decreasing. The upper bound would be simply . I tried to prove this fact but i reached: . But I'm stuck there. Help please.
Thanx
Here is a proof :
PlanetMath: proof of Bernoulli's inequality