# A problem by Arpita Karkera

If \(f\left( x \right) =\frac { { 4 }^{ x } }{ { 4 }^{ x }+2 } \), then \(\left\lfloor f\left( \frac { 1 }{ 2008 } \right) +f\left( \frac { 2 }{ 2008 } \right) +f\left( \frac { 3 }{ 2008 } \right) +...+f\left( \frac { 2007 }{ 2008 } \right) \right\rfloor -1000\) is equal to... (where, \(\left\lfloor . \right\rfloor \) denotes the greatest integer function)