Answer
110
Work Step by Step
Given i = 1 to 5 for $\frac{(i + 2)!}{i!}$
The sum = $\frac{(1 + 2)!}{1!}$ + $\frac{(2 + 2)!}{2!}$ + $\frac{(3 + 2)!}{3!}$ + $\frac{(4 + 2)!}{4!}$ + $\frac{(5 + 2)!}{5!}$
= $\frac{3!}{1!}$ + $\frac{4!}{2!}$ + $\frac{5!}{3!}$ + $\frac{6!}{4!}$ + $\frac{7!}{5!}$
= $\frac{6}{1}$ + $\frac{24}{2}$ + $\frac{120}{6}$ + $\frac{720}{24}$ + $\frac{5040}{120}$
= 6 + 12 + 20 + 30 + 42
= 110
