Assertion (A) : The sum of the series  $\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\mathrm{.......}+\sqrt{1+\frac{1}{{999}^2}+\frac{1}{{1000}^2}}$ is equal to  $\left(\frac{{100}^3-1}{1000}\right)$
Reason (R) : The n^th term of the given series is equal to  $\left(1+\frac{1}{n}-\frac{1}{n+1}\right)$
 

Both (A) and (R) are correct and (R) is the correct explanation of  (A)

Both (A) and (R) are correct and (R) is not the correct explanation of  (A)

(A) is correct but (R) is not correct

(A) is not correct but (R) is correct