Answer
First term (put n = 1) $a_{1}$ = 1
Second term (put n = 2) $a_{2}$ = -2
Third term (put n = 3) $a_{3}$ = $\frac{3}{2}$
Fourth term (put n = 4) $a_{4}$ = -$\frac{2}{3}$
Fifth term (put n = 5) $a_{5}$ = $\frac{5}{24}$
Work Step by Step
Given $a_{n}$ = $(-1)^{(n + 1)}\frac{n}{(n-1)!}$
First term (put n = 1) $a_{1}$ = $(-1)^{(1 + 1)}\frac{1}{(1-1)!}$ = $(-1)^{2}\frac{1}{0!}$ = 1
Second term (put n = 2) $a_{2}$ = $(-1)^{(2 + 1)}\frac{2}{(2-1)!}$ = $(-1)^{3}\frac{2}{1!}$ = -2
Third term (put n = 3) $a_{3}$ = $(-1)^{(3 + 1)}\frac{3}{(3-1)!}$ = $(-1)^{4}\frac{3}{2!}$ = $\frac{3}{2}$
Fourth term (put n = 4) $a_{4}$ = $(-1)^{(4 + 1)}\frac{4}{(4-1)!}$ = $(-1)^{5}\frac{4}{3!}$ = -1$\times$$\frac{2}{3}$ = -$\frac{2}{3}$
Fifth term (put n = 5) $a_{5}$ = $(-1)^{(5 + 1)}\frac{5}{(5-1)!}$ = $(-1)^{6}\frac{5}{4!}$ = $\frac{5}{24}$
