Question

State the limits of the following sequences, or state that the limit does not exist
5, 6 1/2, 5 2/3, 6 1/4, 5 4/5, 6 1/6,..., 6+(-1)^n/n..
Can anyone explain why that the answer is \[\lim_{n \rightarrow \infty}6+(-1)^n/n = 6\]?

Answer 1

HI!!

Answer 2

the larger \(n\) gets the close \(\frac{(-1)^n}{n}\) gets to zero

Answer 3

So it means \[\lim_{n \rightarrow \infty} 6+(0) = 6?\]

Answer 4

\[\lim_{n \rightarrow \infty} 6+\frac{(-1)^n}{n}\]
\[=6+\lim_{n\to \infty}\frac{(-1)^n}{n}=6+0=6\]

Answer 5

okay thanks!

Answer 6

\[\color\magenta\heartsuit\]