The discussion revolves around evaluating the limit of the sequence defined by the expression (-1)^n (n/(n + 1)) as n approaches infinity. Participants are exploring the behavior of this limit, particularly its oscillatory nature.
The conversation is ongoing, with some participants providing insights and others expressing understanding of the oscillation. There appears to be a productive exchange regarding the analytical approach to the limit.
There is a focus on the notation used for limits, with a suggestion to simplify the LaTeX representation. Participants are also considering the implications of the alternating sign in the sequence.
Bashyboy said:Homework Statement
[itex]\stackrel{lim}{n\rightarrow \infty} (-1)^n \frac{n}{n + 1}[/itex]
Homework Equations
The Attempt at a Solution
The answer is that the limit oscillates between -1 and 1, but I was wondering if there was an analytic was of showing this.
\lim_{n\rightarrow \infty}