Assertion: If $\left\{x\right\}$ and $\left[x\right]$ represent fractional part and integral part of $x$ then  $\left[x\right]+\sum _{b=1}^{1000}\frac{\{x+b\}}{1000}=x$

Reason: $\left\{x\right\}=x-\left[x\right]$ and $[x+I ] = \left[x\right] + I$where$I$is an integer 

Assertion is true, reason is true, and reason is not correct explanation for assertion 

Assertion is true, reason is true, and reason is correct explanation for assertion 

Assertion is false, reason is true

Assertion is true, reason is false