Answer
converges to $1$
Work Step by Step
To determine if a sequence converges, see if the limit as $n$ approaches infinity is equal to a constant.
$\lim\limits_{n \to \infty} \frac {\sqrt[3] x}{\sqrt[3] {x} +1}$
Since the highest degree of the polynomials in the numerator and denominator are the same, the limit is simply the ratio between the coefficients of the highest degrees.
$\lim\limits_{n \to \infty} \frac {\sqrt[3] x}{\sqrt[3] {x} +1}=\frac {1}{1}=1$
Therefore, the sequence converges to 1.
