Answer
$a_1=\frac{1}{2}$
$a_2=-\frac{2}{3}$
$a_3=\frac{3}{4}$
$a_4=-\frac{4}{5}$
$a_{100}=-\frac{100}{101}$
Work Step by Step
We are given:
$a_{n}= (-1)^{n+1}\frac{n}{n+1}= \frac{(-1)^{n+1}n}{n+1}$
We evaluate:
$a_1=\frac{(-1)^{2}\ 1}{1+1}=\frac{1}{2}$
$a_2=\frac{(-1)^{3}\ 2}{2+1}=-\frac{2}{3}$
$a_3=\frac{(-1)^{4}\ 3}{3+1}=\frac{3}{4}$
$a_4=\frac{(-1)^{5}\ 4}{4+1}=-\frac{4}{5}$
$a_{100}= \frac{(-1)^{101}\ 100}{101}=-\frac{100}{101}$
