Chứng minh rằng:
\(\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+...+\dfrac{1}{\sqrt{225}}< 28\)
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 rằng \(\dfrac{1}{2}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{4\sqrt{3}}+...+\dfrac{1}{2009\sqrt{2008}}< 2\)
Chứng minh rằng:
\(\dfrac{87}{89}< \dfrac{1}{2\sqrt{1}}+\dfrac{1}{3\sqrt{2}}+...+\dfrac{1}{2011\sqrt{2010}}< \dfrac{88}{45}\)
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
Bài 1. Tìm x, y, z biết: \(\sqrt{x-a}+\sqrt{y-b}+\sqrt{z-c}=\dfrac{1}{2}\left(x+y+z\right)\) (trong đó, a + b + c = 3)
Bài 2.
a) Chứng minh rằng: \(2\left(\sqrt{n+1}-\sqrt{n}\right)< \dfrac{1}{\sqrt{n}}< 2\left(\sqrt{n}-\sqrt{n-1}\right)\)
b/ Cho S = \(1+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+...+\dfrac{1}{\sqrt{100}}\). Chứng minh rằng: 18<S<19
Chứng minh rằng: \(1+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+.....+\dfrac{1}{\sqrt{n}}>2\left(\sqrt{n+1}-1\right)\)Với n là số nguyên
Chứng minh : \(\dfrac{1}{2\sqrt{1}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{4\sqrt{3}}+...+\dfrac{1}{2005\sqrt{2004}}< 2\)