Các câu hỏi tương tự
Giải pt :\(\frac{\sqrt{x-2009}-1}{x-2009}+\frac{\sqrt{y-2010}-1}{y-2010}+\frac{\sqrt{z-2011}-1}{z-2011}=\frac{3}{4}\)
Tính :a ) Sfrac{1}{sqrt{1}sqrt{3}}+frac{1}{sqrt{3}+sqrt{5}}+frac{1}{sqrt{5}+sqrt{7}}+.....+frac{1}{sqrt{2017}+sqrt{2019}}b ) Sfrac{1}{sqrt{2}+sqrt{4}}+frac{1}{sqrt{4}+sqrt{6}}+....+frac{1}{sqrt{100}+sqrt{102}}c ) Sfrac{1}{sqrt{1}+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+.....+frac{1}{sqrt{100}+sqrt{101}}d ) Sfrac{1}{sqrt{3}+sqrt{6}}+frac{1}{sqrt{6}+sqrt{9}}+frac{1}{sqrt{9}+sqrt{12}}+....+frac{1}{sqrt{2016}+sqrt{2019}}
Đọc tiếp
Tính :
a ) \(S=\frac{1}{\sqrt{1}\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+.....+\)\(\frac{1}{\sqrt{2017}+\sqrt{2019}}\)
b ) \(S=\frac{1}{\sqrt{2}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{6}}+....+\frac{1}{\sqrt{100}+\sqrt{102}}\)
c ) \(S=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.....+\frac{1}{\sqrt{100}+\sqrt{101}}\)
d ) \(S=\frac{1}{\sqrt{3}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{12}}+....+\frac{1}{\sqrt{2016}+\sqrt{2019}}\)
Tính C= \(\frac{1}{1\sqrt{2}+2\sqrt{1}}+\frac{1}{2\sqrt{3}+3\sqrt{2}}+...............+\frac{1}{2011\sqrt{2012}+2012\sqrt{2011}}\)
Chứng minh : \(\frac{1}{\left(\sqrt{2}+\sqrt{5}\right)^3}+\frac{1}{\left(\sqrt{5}+\sqrt{8}\right)^3}\)\(+...+\frac{1}{\left(\sqrt{2006}+\sqrt{2009}\right)^3}\)\(< \frac{11}{135}\)
Tính :
a ) \(S=\frac{1}{3\sqrt{1}+3\sqrt{3}}+\frac{1}{3\sqrt{3}+3\sqrt{5}}+...+\)\(\frac{1}{3\sqrt{2017}+3\sqrt{2019}}\)
b ) \(S=\frac{7}{\sqrt{2.2}+\sqrt{2.3}}+\frac{7}{\sqrt{2.3}+\sqrt{2.4}}\)\(+...+\frac{7}{\sqrt{2.2018}+\sqrt{2.2019}}\)
tính:\(\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{9}}\)
1 + \(\frac{1}{\sqrt{2}}\)+ \(\frac{1}{\sqrt{3}}\)+ ... + \(\frac{1}{\sqrt{2009}}\)< \(2\sqrt{2009}\)
Tính P = \(\frac{4+\sqrt{3}}{\sqrt{1}+\sqrt{3}}+\frac{8+\sqrt{15}}{\sqrt{3}+\sqrt{5}}+...+\frac{2n+\sqrt{n^2-1}}{\sqrt{n-1}+\sqrt{n+1}}+...+\frac{240+\sqrt{14399}}{\sqrt{119}+\sqrt{121}}\)
1-a,\(A=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{n-1}+\sqrt{n}}\)
b,\(B=\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)