There's a pattern!

Number Theory Level pending

\[ \frac { 2016! }{ 2015!+2014! } +\frac { 2015! }{ 2014!+2013! } +\frac { 2014! }{ 2013!+2012! } +\frac { 2013! }{ 2015!+2014! } +...+\frac { 2! }{ 1!+0! } \]

What is the sum of the digits of the sum above?

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