Question

calculus- Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.

Answer 1

\[\lim_{n \rightarrow \infty} (-1^n)\sin(8/n)\]

Answer 2

how do i do this?

Answer 3

presuming you meant \((-1)^n\) rather than \((-1^n)\):
observe that \(\{a_n\}\) converges iff \(\{|a_n|\}\) so we can toss out the alternating factor. since \(\sin(x)\) is continuous we can pass the limit inside:$$\lim_{n\to\infty}\sin(8/n)=\sin(\lim_{n\to\infty}8/n)=\sin(0)=0$$