Answer
The given series is convergent
Work Step by Step
$\Sigma^{\infty}_{n=1} \frac{1}{n^{3}}$
$a_{n} = \frac{1}{n^{3}}$
partial sum $s_{n} = a_{1} + a_{2} +...+a_{n}$
$n=1$ $a_{1}= 1.00$ $s_{1}=1.00$
$n=2$ $a_{2}=0.125$ $s_{2}=1.125$
$n=3$ $a_{3}=0.03704$ $s_{3}=1.1620$
$n=4$ $a_{4}=0.01563$ $s_{4}=1.1777$
$n=5$ $a_{5}=0.008$ $s_{5}=1.1857$
$n=6$ $a_{6}=0.00463$ $s_{6}=1.1903$
$n=7$ $a_{7}=0.00292$ $s_{7}=1.1932$
$n=8$ $a_{8}=0.00195$ $s_{8}=1.1952$
We observe that all the terms of the series are approaching to approximately 1.2
Therefore the given series is convergent.
