#### Answer

$a_1 = 0.9$
$a_2 = 0.99$
$a_3 = 0.999$
$a_4 = 0.9999$
Converges. The limit of the sequence seems to be $1$.

#### Work Step by Step

$a_n = 1-10^{-n}$
$a_1 = 1 - 10^{-1} = 0.9$
$a_2 = 1 - 10^{-2} = 0.99$
$a_3 = 1 - 10^{-3} = 0.999$
$a_4 = 1 - 10^{-4} = 0.9999$
Converges and approaches $1$. The term $10^{-n}$ seems to approach zero as $n$ increases and $1-0=1$. Alternatively, simply looking at the terms tells us that the term approaches $1$ as $n$ increases.