Calculate this when you’re brushing teeth

$\quad \left( n+1 \right) \left( n+2 \right) \left( n+3 \right) \left( n+4 \right) \\ =\dfrac { 5\left( n+1 \right) \left( n+2 \right) \left( n+3 \right) \left( n+4 \right) }{ 5 } \\ =\dfrac { \left( n+1 \right) \left( n+2 \right) \left( n+3 \right) \left( n+4 \right) \left[ \left( n+5 \right) -n \right] }{ 5 } \\ =\dfrac { \left( n+1 \right) \left( n+2 \right) \left( n+3 \right) \left( n+4 \right) \left( n+5 \right) -n\left( n+1 \right) \left( n+2 \right) \left( n+3 \right) \left( n+4 \right) }{ 5 } \\ \quad\dfrac{1\times2\times3\times4+2\times3\times4\times5+\dots+2016\times2017\times2018\times2019}{2016\times2017\times2018\times2019} \\=\dfrac {1\times2\times3\times4\times5-0\times1\times2\times3\times4+2\times3\times4\times5\times6-1\times2\times3\times4\times5+\dots+2016\times2017 \times2018 \times2019 \times2020 -2015\times2016\times2017\times2018\times2019}{5\times2016\times2017\times2018\times2019} \\ = \dfrac{2016 \times2017 \times2018 \times2019 \times2020}{5\times2016\times2017\times2018\times2019} \\ =\boxed{404}$

$\frac{1 \times 2 \times 3 \times 4+2 \times 3 \times 4 \times 5+...+2016 \times 2017 \times 2018 \times 2019}{2016 \times 2017 \times 2018 \times 2019}$ = $\frac{5(1 \times 2 \times 3 \times 4+2 \times 3 \times 4 \times 5+...+2016 \times 2017 \times 2018 \times 2019)}{5(2016 \times 2017 \times 2018 \times 2019)}$ = $\frac{1 \times 2 \times 3 \times 4 \times 5+2 \times 3 \times 4 \times 5 \times 5+...+2016 \times 2017 \times 2018 \times 2019 \times 5}{2016 \times 2017 \times 2018 \times 2019 \times 5}$ = $\frac{(1+5)(2 \times 3 \times 4 \times 5)+...+2016 \times 2017 \times 2018 \times 2019 \times 5}{2016 \times 2017 \times 2018 \times 2019 \times 5}$ = $\frac{2 \times 3 \times 4 \times 5 \times 6+...+2016 \times 2017 \times 2018 \times 2019 \times 5}{2016 \times 2017 \times 2018 \times 2019 \times 5}$ = $\frac{2016 \times 2017 \times 2018 \times 2019 \times 2020}{2016 \times 2017 \times 2018 \times 2019 \times 5}$ = $404$