sum of seriess..!!

T_{n}=\sqrt{1+\frac{1}{n^2}+\frac{1}{(n+1)^2}} \\ T_{n}=\sqrt{\frac{1}{n^2}+\frac{1}{(n+1)^2}-\frac{2}{n(n+1)}+2(\frac{1}{n}-\frac{1}{n+1})+1}\\ T_{n}=\sqrt{(\frac{1}{n}+\frac{1}{(n+1)})^2+2(\frac{1}{n}-\frac{1}{n+1})+1} \\ \\ \boxed{T_n=\frac{1}{n}-\frac{1}{n+1}+1} \\ \sum_{n=1}^{2007}{T_n}=2007+1-\frac{1}{2008} \\ \boxed{Ans.=2008-\frac{1}{2008}}