Các câu hỏi tương tự
So sánh A và B:
\(A=\sqrt{2015^2-1}-\sqrt{2014^2-1}\)
\(B=\frac{2.2014}{\sqrt{2015^2-1}+\sqrt{2014^2-1}}\)
so sánh \(\sqrt{2015^2-1}-\sqrt{2014^2-1}\) và \(\frac{2.2014}{\sqrt{2015^2-1}+\sqrt{2014^2-1}}\)
a)
\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+....+\frac{1}{\sqrt{24}+\sqrt{25}}\)
b)
\(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+....+\frac{1}{\sqrt{2006}+\sqrt{2007}}\)
So sánh: \(\sqrt{2007}-\sqrt{2006}\) và \(\frac{1}{2\sqrt{2006}}\)
Bài 1. So sánha) sqrt{2009}-sqrt{2008}và sqrt{2007}-sqrt{2006}b) sqrt{11+sqrt{96}}và frac{2sqrt{2}}{1+sqrt{2}-sqrt{3}}Bài 2. Tính tổngTfrac{1}{1-sqrt{2}}-frac{1}{sqrt{2}-sqrt{3}}+frac{1}{sqrt{3}-sqrt{4}}-...+frac{1}{sqrt{2007}-sqrt{2008}}Dfrac{1}{2sqrt{1}+1sqrt{2}}+frac{1}{3sqrt{2}+2sqrt{3}}+frac{1}{4sqrt{3}+3sqrt{4}}+...+frac{1}{120sqrt{121}+121sqrt{120}}ai cứu mk ikk
Đọc tiếp
Bài 1. So sánh
a) \(\sqrt{2009}-\sqrt{2008}\)và \(\sqrt{2007}-\sqrt{2006}\)
b) \(\sqrt{11+\sqrt{96}}\)và \(\frac{2\sqrt{2}}{1+\sqrt{2}-\sqrt{3}}\)
Bài 2. Tính tổng
\(T=\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...+\frac{1}{\sqrt{2007}-\sqrt{2008}}\)
\(D=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{120\sqrt{121}+121\sqrt{120}}\)
ai cứu mk ikk
Tính
a) \(\frac{1+3\sqrt{2}-2\sqrt{3}}{\sqrt{6}+\sqrt{3}+\sqrt{2}}\)
b) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3+\sqrt{4}}}+...+\frac{1}{\sqrt{2006}+\sqrt{2007}}\)
CM:a)\(2\left(\sqrt{a}-\sqrt{b}\right)< \frac{1}{\sqrt{b}}< 2\left(\sqrt{a}-\sqrt{b}\right)biet:a=b+1=c+2\left(c>0\right).\)
b)\(CM:B=\sqrt{1+2014^2+\frac{2014^2}{2015^2}}+\frac{2014}{2015}nguyen\)
Tính gía trị biểu thức:
\(A=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+....+\frac{1}{2014\sqrt{2013}+2013\sqrt{2014}}+\frac{1}{2015\sqrt{2014}+2014\sqrt{2015}}\)
Cho M=\(\frac{\sqrt{2}-\sqrt{1}}{1+1}+\frac{\sqrt{3}-\sqrt{2}}{2+3}+\frac{\sqrt{4}-\sqrt{3}}{3+4}+...+\frac{\sqrt{2015}-\sqrt{2014}}{2014+2015}\)
Hãy so sánh M với 1/2