\(A=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{120}+\sqrt{121}}\)
\(B=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{35}}\)
Chứng minh B>A
cho A= \(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{120}+\sqrt{121}}\); B = \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{35}}\)
Chứng minh A<B
cho \(A=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{120}+\sqrt{121}}\)
\(B=\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{35}}\)
Chứng minh rằng A<B
1. Chứng minh rằng
\(S=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{5}+\sqrt{6}}+...+\frac{1}{\sqrt{79}+\sqrt{80}}>4\)
2. Chứng minh rằng
\(\frac{\sqrt{1}}{1}+\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}+...+\frac{\sqrt{200}}{200}>10+5\sqrt{2}\)
3. Cho a >= 1, b >= 1, chứng minh rằng
\(a\sqrt{b-1}+b\sqrt{a-1}\le ab\)
4. Giải phương trình
\(\sqrt{\left(x^2-2x+5\right)\left(x^2-4x\right)+7}+x^2-3x+6\)
LÀM PHIỀN M.N GIÚP MK. XIN CẢM ƠN !!!
\(A=\frac{\sqrt{2}-\sqrt{1}}{2+1}+\frac{\sqrt{3}-\sqrt{2}}{3+2}+...+\frac{\sqrt{36}-\sqrt{35}}{36+35}\)
chứng minh A < 5/2
a, Chứng minh
\(\frac{1}{\left(n+1\right).\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}\)
b, Áp dụng
\(S=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{3\sqrt{4}+4\sqrt{3}}......+\frac{1}{400\sqrt{399}+399\sqrt{400}}\)
a)Cho a>b>0 chứng minh rằng \(\frac{1}{a+b}\le\frac{1}{2\sqrt{ab}}\)
b) Chứng minh \(\frac{\sqrt{2}-\sqrt{1}}{3}+\frac{\sqrt{3}-\sqrt{2}}{5}+\frac{\sqrt{4}-\sqrt{3}}{7}+...+\frac{\sqrt{2011}-\sqrt{2010}}{4021}< \frac{1}{2}\)
chứng minh B=\(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{5}+\sqrt{6}}+...+\frac{1}{\sqrt{78}+\sqrt{79}}>4\)
Chứng minh
\(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}.\sqrt{3}}+\frac{1}{\sqrt{3}.\sqrt{4}}+...+\frac{1}{\sqrt{2004}.\sqrt{2005}}< 2\)