Answer
15
Work Step by Step
given i = 1 to 5 in $\frac{i!}{(i - 1)!}$
Then the sum = $\frac{1!}{(1 - 1)!}$ + $\frac{2!}{(2 - 1)!}$ + $\frac{3!}{(3 - 1)!}$ + $\frac{4!}{(4 - 1)!}$ + $\frac{5!}{(5 - 1)!}$
= $\frac{1!}{(0)!}$ + $\frac{2!}{(1)!}$ + $\frac{3!}{(2)!}$ + $\frac{4!}{(3)!}$ + $\frac{5!}{(4)!}$
= $\frac{1}{1}$ + $\frac{2}{1}$ + $\frac{6}{2}$ + $\frac{24}{6}$ + $\frac{120}{24}$
= 1 + 2 + 3 + 4 + 5
= 15
