Find the value of

Find the value of :

$$\sqrt{1+\frac{1}{1^2 }+\frac{1}{2^2 }  }+\sqrt{1+\frac{1}{2^2 }+\frac{1}{3^2 }  }+............\sqrt{1+\frac{1}{999^2}+\frac{1}{1000^2 }  }$$

I am unable to identify the sequence.This does not seem to be an A.P.

Please show all the steps.

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