Answer
$a_n=${2.1111, 2.2346, 2.3717, 2.5242, 2.6935, 2.8817, 3.0908, 3.323, 3.5812, 3.8680}
This sequence is divergent
Work Step by Step
Given: $a_n=1+\frac{{10}^{n}}{{9}^{n}}$
Substitute the values 1 to 10 in the place of n:
$a_n=${2.1111, 2.2346, 2.3717, 2.5242, 2.6935, 2.8817, 3.0908, 3.323, 3.5812, 3.8680}
From inspection this sequence does not converge
If you take
$\frac{{10}^{n}}{{9}^{n}}$
=${(\frac{10}{9})}^{n}$
Therefore r=$\frac{10}{9}$>1
This means that it is divergent