Ta có:
$\dfrac{1}{\sqrt{n}+\sqrt{n+4}}=\dfrac{\sqrt{n}-\sqrt{n+4}}{\left(\sqrt{n}+\sqrt{n+4}\right)\left(\sqrt{n}-\sqrt{n+4}\right)}=\dfrac{\sqrt{n}-\sqrt{n+4}}{4}$
$\Rightarrow B=\left(\dfrac{1}{\sqrt{1}+\sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{9}}+...+\dfrac{1}{\sqrt{2009}+\sqrt{2013}}\right)+\left(\dfrac{1}{\sqrt{2}+\sqrt{6}}+\dfrac{1}{\sqrt{6}+\sqrt{10}}+...+\dfrac{1}{\sqrt{2010}+\sqrt{2014}}\right)$
$\Rightarrow B=\left(\dfrac{\sqrt{1}-\sqrt{5}}{4}+\dfrac{\sqrt{5}-\sqrt{9}}{4}+...+\dfrac{\sqrt{2009}-\sqrt{2013}}{4}\right)+\left(\dfrac{\sqrt{2}-\sqrt{6}}{4}+\dfrac{\sqrt{6}-\sqrt{10}}{4}+...+\dfrac{\sqrt{2010}-\sqrt{2014}}{4}\right)$
$\Rightarrow B=\dfrac{\sqrt{1}-\sqrt{2013}+\sqrt{2}-\sqrt{2014}}{4}$
Vậy $B \approx -21,83247$
