Answer
$2.1111, 2.2346, 2.3717, 2.5242, 2.6935, 2.8817, 3.0908, 3.3231, 3.5812, 3.8680$
The sequence has no limit or it diverges.
Work Step by Step
It is given a sequence formulated by $a_n=1+\frac{10^n}{9^n}$
Substituting $n$ from 1 to 10, we get the first ten terms of the sequence:
$2.1111, 2.2346, 2.3717, 2.5242, 2.6935, 2.8817, 3.0908, 3.3231, 3.5812, 3.8680$
Observing these terms, the sequence does not appear to have a limit. Why? Because as $n$ goes to infinity, the value of $\frac{10^n}{9^n}=(\frac{10}{9})^n$ also goes to infinity.
So, the sequence diverges.
Thus, $\lim\limits_{n \to \infty}a_n=\infty$.
