If $g\left(x\right)=\left[x\right]+\sum _{a=1}^{2012}\frac{x+a-[x+a]}{2012}$   then the value of  $g\left(100\right)$  ? (Note : [] denote greatest integer function)

$g\left(x\right)=\left[x\right]+\sum _{a=1}^{2012}\frac{(x+a)-\left(\right[x]+a)}{2012}$

$=\left[x\right]+\frac{1}{2012}\sum _{a=1}^{2012}(x-[x\left]\right)$

$=\left[x\right]+\frac{1}{2012}\left(2012\right)(x-[x\left]\right)$

$\therefore g\left(x\right)=\left[x\right]+(x-[x\left]\right)$

$\therefore g\left(x\right)=x\Rightarrow g\left(100\right)=100$