A positive integer n satisfies the equation (n+1) !+(n+2) !=440 \cdot n !. What is the sum of the digits of n ?

**Answer Choices**

A. 2

B. 5

C. 10

D. 12

E. 15

A positive integer n satisfies the equation (n+1) !+(n+2) !=440 \cdot n !. What is the sum of the digits of n ?

**Answer Choices**

A. 2

B. 5

C. 10

D. 12

E. 15