Answer
Convergent
Work Step by Step
$n_{1}$ = $\frac{1}{1}$ = 1
$n_{1}$ = $\frac{1}{2^{3}}$ = 1/8
$n_{1}$ = $\frac{1}{3^{3}}$ = 1/27
$n_{1}$ = $\frac{1}{4^{3}}$ = 1/64
$n_{1}$ = $\frac{1}{5^{3}}$ = 1/125
$n_{1}$ = $\frac{1}{6^{3}}$ = 1/216
$n_{1}$ = $\frac{1}{7^{3}}$ = 1/243
$n_{1}$ = $\frac{1}{8^{3}}$ = 1/512
To decide whether the series is convergent or divergent, you can use the p-series test. The main formula is $\frac{1}{n^{3}}$ where $p =3$. Since $3 > 1$, it holds that the series is convergent.