Answer
$\displaystyle a_1=0$
$\displaystyle a_2=\frac{1}{4}$
$\displaystyle a_3=0$
$\displaystyle a_4=\frac{1}{32}$
$\displaystyle a_{10}=\frac{1}{500}$
Work Step by Step
We are given:
$\displaystyle a_{n}= \frac{(-1)^{n}+1}{n^{3}}$
We evaluate:
$\displaystyle a_1= \frac{(-1)^{1}+1}{1^{3}}=\frac{-1+1}{1}=0$
$\displaystyle a_2= \frac{(-1)^{2}+1}{2^{3}}=\frac{2}{8}=\frac{1}{4}$
$\displaystyle a_3=\frac{(-1)^{3}+1}{3^{3}}=\frac{-1+1}{27}=0$
$\displaystyle a_4= \frac{(-1)^{4}+1}{4^{3}}=\frac{2}{64}=\frac{1}{32}$
$\displaystyle a_{10}= \frac{(-1)^{10}+1}{10^{3}}=\frac{1+1}{1000}=\frac{1}{500}$
