[Toán 9] Chứng minh

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hoangtubongdem5

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letsmile519

1+21+2 \geq 222\sqrt{2}
2+32+3\geq 262\sqrt{6}

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2−11+2+3−23+2+...+36−3535+36\frac{\sqrt{2}-\sqrt{1}}{1+2}+\frac{\sqrt{3}-\sqrt{2}}{3+2}+...+\frac{\sqrt{36}-\sqrt{35}}{35+36}\leq 2−12.2+3−22.6+...+36−352.35.36\frac{\sqrt{2}-\sqrt{1}}{2.\sqrt{2}}+\frac{\sqrt{3}-\sqrt{2}}{2.\sqrt{6}}+...+\frac{\sqrt{36}-\sqrt{35}}{2.\sqrt{35}.\sqrt{36}}

2−11+2+3−23+2+...+36−3535+36\frac{\sqrt{2}-\sqrt{1}}{1+2}+\frac{\sqrt{3}-\sqrt{2}}{3+2}+...+\frac{\sqrt{36}-\sqrt{35}}{35+36}\leq 12(1−12+12−13+...+135−136)\frac{1}{2}(1-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{35}}-\frac{1}{\sqrt{36}})=12(1−16)=512\frac{1}{2}(1-\frac{1}{6})=\frac{5}{12}
 
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