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 $$\lim_{n \rightarrow \infty}6+(-1)^n/n = 6$$?

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 $$\lim_{n \rightarrow \infty}6+(-1)^n/n = 6$$?

misty1212 · Answer

HI!!

misty1212 · Answer

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

anonymous · Answer

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

misty1212 · Answer

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

anonymous · Answer

okay thanks!

misty1212 · Answer

$$\color\magenta\heartsuit$$