Hi Spartan,
If you consider the first term-
$$\sqrt{1+1/1^2+1/2^2}$$ = $$\sqrt{9/4}$$ = 3/2

Second term: $$\sqrt{1+1/2^2+1/3^2}$$ = $$\sqrt{49/36}$$ = 7/6

First term + Second term = 3/2 + 7/6 = (9+7)/6 = 16/6 = 8/3 = 3 - 1/3
Similarly, when you consider the third term 
Third term : $$\sqrt{1+1/3^2+1/4^2}$$ = $$\sqrt{169/144}$$ = 13/12
Now, if you add First term + Second term + Third term = 3/2  + 7/6  + 13/12
=> 15/4, or we can say 4-1/4
That means, if we add all the terms of this series, its sum will be 2008 - 1/2008
I hope this helps!

thanksss

Hi Spartan,
We are glad it helped you; please let us know if you have any further doubts. Regards

Hi Sprtan,
I've already answered your doubt by explaining in detail. Please go through the explanation given by me and let me know if your doubt still persists. Regards