Školjka

%V0 Dokažite da je $$ \sqrt{1+\dfrac{1}{1^2}+\dfrac{1}{2^2}}+ \sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\ldots + \sqrt{1+\dfrac{1}{2004^2}+\dfrac{1}{2005^2}}=2005-\dfrac{1}{2005}. $$