Chứng minh \(\dfrac{\sqrt{2}-\sqrt{1}}{3}+\dfrac{\sqrt{3}-\sqrt{2}}{5}+\dfrac{\sqrt{4}-\sqrt{3}}{7}+...+\dfrac{\sqrt{2011}-\sqrt{2010}}{4021}< \dfrac{1}{2}\)
giúp mk vs
Cho A=\(\dfrac{1}{\sqrt{2}}\)+\(\dfrac{1}{\sqrt{3}}\)+....+\(\dfrac{1}{\sqrt{2025}}\)
Chứng minh rằng 2(\(\sqrt{2026}\)-\(\sqrt{2}\)) <A>88
Chứng minh bất đẳng thức với n nguyên dương
\(\dfrac{1}{2}\)+\(\dfrac{1}{3\sqrt[2]{2}}\)+...+\(\dfrac{1}{2010\sqrt[2]{2009}}\)<\(\dfrac{89}{45}\)
\(\dfrac{\sqrt{x-2009}-1}{x-2009}+\dfrac{\sqrt{y-2010}-1}{y-2010}+\dfrac{\sqrt{z-2011}-1}{z-2011}=\dfrac{3}{4}\)
giải pt
Chứng minh rằng \(\dfrac{1}{2}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{4\sqrt{3}}+...+\dfrac{1}{2009\sqrt{2008}}< 2\)
Tính:
1) A=\(\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+...+\dfrac{1}{2010\sqrt{2009}+2009\sqrt{2010}}\)
2) B=\(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+...+\dfrac{1}{\sqrt{2006}+\sqrt{2007}}\)
Chứng Minh
\(\dfrac{1+\dfrac{\sqrt{3}}{2}}{1+\sqrt{1+\dfrac{\sqrt{3}}{2}}}\) + \(\dfrac{1-\dfrac{\sqrt{3}}{2}}{1-\sqrt{1-\dfrac{\sqrt{3}}{2}}}\) = 1
Chứng minh rằng:
\(\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+...+\dfrac{1}{\sqrt{225}}< 28\)
