Find the sum of the series 1⋅2+2⋅3+3⋅4+⋯+n(n+1)1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \dots + n(n+1)1⋅2+2⋅3+3⋅4+⋯+n(n+1) in terms of nnn.
n(n+1)(n+2)3\frac{n(n+1)(n+2)}{3}3n(n+1)(n+2)
n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6}6n(n+1)(2n+1)
n(n+1)(n+2)(n+3)4\frac{n(n+1)(n+2)(n+3)}{4}4n(n+1)(n+2)(n+3)
n(n+1)(2n+4)3\frac{n(n+1)(2n+4)}{3}3n(n+1)(2n+4)