Find the Right Part of the Equality $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) =$

Multiple Choice

Find the right part of the equality. $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) =$ ________

A) $\frac { n ^ { 2 } ( n + 3 ) } { 4 }$
B) $\frac { n ( n + 1 ) ( n + 2 ) } { 3 }$
C) $\frac { n \left( 4 n ^ { 2 } + 6 n - 1 \right) } { 3 }$
D) $\frac { n ^ { 2 } ( n - 1 ) ( n + 3 ) } { 2 }$