The sequence defined by an = (n/(n+2))^n converges to a finite limit as n approaches infinity. While some participants in the discussion initially believed the sequence to be divergent, it is established that the limit exists and is finite. The confusion arises from the distinction between sequences and series; the sequence converges, whereas the series diverges. This clarification is crucial for accurately understanding the behavior of the sequence.
PREREQUISITESStudents studying calculus, particularly those focusing on sequences and series, as well as educators seeking to clarify the concepts of convergence and divergence in mathematical analysis.
cathy said:Homework Statement
an= (n/n+2)^nThe Attempt at a Solution
I was told this was convergent and I need to find the limit of the sequence. How do I do this, as I seem to keep getting that this is divergent. Isn't it divergent to infinity? Or am I missing something?