Use Mathematical Induction to Solve for All Positive Integers N $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = ?$

Multiple Choice

Use mathematical induction to solve for all positive integers n. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = ?$

A) $\frac { n ( 2 n + 13 ) } { 6 }$
B) $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 4 }$
C) $\frac { n ( n + 1 ) ( n + 13 ) } { 6 }$
D) $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$
E) $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 2 }$