Tính
1) \(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{1999\sqrt{1998}+1998\sqrt{1999}}\)
2) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{1998}+\sqrt{1999}}\)
Tính \(A=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{1999\sqrt{1998}+1998\sqrt{1999}}\)
So sánh: Sqrt (1998) + sqrt (2000) và 2*sqrt (1999)
Tính
N=\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{1999\sqrt{1998}+1998\sqrt{1999}}\)
giúp mình với
tính:A=\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{2000\sqrt{1999}+1999\sqrt{2000}}\)
Chứng minh:\(\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+...+\frac{1}{1999\sqrt{1998}}< 2\)<2
Chứng minh rằng :\(\sqrt{2\sqrt{3\sqrt{4\sqrt{5...\sqrt{2000}}}}}\)<3
CMR:\(\sqrt{2\sqrt{3\sqrt{4\sqrt{5...\sqrt{2000}}}}}\)<3
\(\frac{3-\sqrt{3+\sqrt{3+\sqrt{3+...+\sqrt{3}}}}}{6-\sqrt{3+\sqrt{3+\sqrt{3+...+\sqrt{3}}}}}\)
cm M nhỏ hơn \(\frac{1}{4}\)