Answer
$a_{1}=\displaystyle \frac{1}{2}$,
$a_{2}=-\displaystyle \frac{2}{3}$,
$a_{3}=\displaystyle \frac{3}{4}$,
$a_{4}=-\displaystyle \frac{4}{5}$,
$a_{100}=-\displaystyle \frac{100}{101}$
Work Step by Step
$a_{n}=\displaystyle \frac{(-1)^{n+1}n}{n+1}$.
$a_{1}=\displaystyle \frac{(-1)^{2}\cdot 1}{1+1}=\frac{1}{2}$,
$a_{2}=\displaystyle \frac{(-1)^{3}\cdot 2}{2+1}=-\frac{2}{3}$,
$a_{3}=\displaystyle \frac{(-1)^{4}\cdot 3}{3+1}=\frac{3}{4}$,
$a_{4}=\displaystyle \frac{(-1)^{5}\cdot 4}{4+1}=-\frac{4}{5}$,
$a_{100}=\displaystyle \frac{(-1)^{101}\cdot 100}{101}=-\frac{100}{101}$
