$\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{\frac{1}{1}+\frac{1}{3^2}+\frac{1}{4^2}}………….\sqrt{1+\frac{1}{2007^2}+\frac{1}{2008^2}}$

TITA type i.e. Type In The Answer type

2007

In first bracket, there is 1 * 2 in the denominator.

In the second bracket, there is 2*3 in the denominator

In the third bracket, there will be 3*4 in the denominator.

And in the last bracket, there is 2007*2008 in the denominator.

So, no of terms are from 1 to 2007 (2007 terms) or from 2 to 2008 (still 2007 terms).

So, 1+1+1+1+1+…(2007 times) = 2007