Answer
$1.0000, 2.5000, 1.6667, 2.2500, 1.8000, 2.1667, 1.8571, 2.1250, 1.8889, 2.1000$
$\lim\limits_{n \to \infty}a_n=2$
Work Step by Step
It is given a sequence formulated by $a_n=2+\frac{(-1)^n}{n}$.
Substituting $n$ from 1 to 10, we get the first ten terms of the sequence:
$1.0000, 2.5000, 1.6667, 2.2500, 1.8000, 2.1667, 1.8571, 2.1250, 1.8889, 2.1000$
Using these terms, the sequence appears to have a limit.
Calculate the limit:
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}2+\frac{(-1)^n}{n}$
$=2+0$
$=2$
So, the limit of the sequence is $2$.
