Question

\(\frac{1}{\sqrt{1}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{9}}+...+\frac{1}{\sqrt{953}+\sqrt{957}}+\frac{1}{\sqrt{957}+\sqrt{961}}\)rút gọn 

Answer 1

\(=\frac{1}{\sqrt{1}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{9}}+...+\frac{1}{\sqrt{957}+\sqrt{961}}\)

\(=\sqrt{5}-\sqrt{1}+\sqrt{9}-\sqrt{5}+...+\sqrt{961}-\sqrt{957}\)

\(=-\sqrt{1}+\sqrt{961}=\sqrt{961}-1=31-1=30\)

Answer 2

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