The discussion revolves around the convergence of the ratio xn/xn+1 given that the sequence xn approaches infinity. Participants explore the validity of the original statement and seek to establish a rigorous proof or counterexamples.
The conversation is ongoing, with participants exploring different interpretations of the problem. Some have provided insights into the nature of the sequence and its behavior, while others are still grappling with the implications of the correction regarding the ratio. There is no explicit consensus yet.
A recent clarification from the instructor indicated a typo in the problem statement, changing the ratio to xn/(xn+1), which has shifted the focus of the discussion significantly.
bballninja said:I'm pretty sure it's true, since each successive term of the sequence will be larger or equal to the previous, so xn/xn+1 should always be ≤ 1
bballninja said:Well would I be able to claim that it is non-decreasing monotone, and show that it is bounded which implies convergence?
bballninja said:Ahh I'm so sorry haha. The instructor just emailed us that there was a typo and the ratio should actually be xn / (xn+1). This makes more sense now. Thanks for your help though