Đáp án:
`B=11`
Giải thích các bước giải:
Ta có:
`B=\frac{1}{1+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{13}}+...+\frac{1}{\sqrt{2021}+\sqrt{2025}}`
`=\frac{\sqrt{5}-1}{(\sqrt{5}+1)(\sqrt{5}-1)}+\frac{\sqrt{9}-\sqrt{5}}{(\sqrt{9}+\sqrt{5})(\sqrt{9}-\sqrt{5})}+...+\frac{\sqrt{2025}-\sqrt{2021}}{(\sqrt{2025}+\sqrt{2021})(\sqrt{2025}-\sqrt{2021})}`
`=\frac{\sqrt{5}-1+\sqrt{9}-\sqrt{5}+...+\sqrt{2025}-\sqrt{2021}}{4}`
`=\frac{-1+\sqrt{2025}}{4}`
`=11`
