Các câu hỏi tương tự
CMR: \(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{225}}< 28\)
CMR: \(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+....+\frac{1}{\sqrt{225}}< 28\)
Chứng minh rằng:
a) \(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{225}}>28\)
CMR \(\frac{1}{\sqrt{2}}\)+\(\frac{1}{\sqrt{3}}\)+.....+\(\frac{1}{\sqrt{225}}\)<28
Tính
\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{225\sqrt{224}+224\sqrt{225}}\)
So sánh
M=\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{224}+\sqrt{225}}\)
N=\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{63}}\)
tính :
\(A=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
\(B=\frac{1}{\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{10}}+....+\frac{1}{\sqrt{220}+\sqrt{225}}\)
CM các biểu thức sau là một số nguyên:
a/\(\frac{1+\frac{\sqrt{3}}{2}}{1+\sqrt{1+\frac{\sqrt{3}}{2}}}+\frac{1-\frac{\sqrt{3}}{2}}{1-\sqrt{1-\frac{\sqrt{3}}{2}}}\)
b/\(\left(\frac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}+\frac{6-4\sqrt{2}}{\sqrt{2}-\sqrt{6-4\sqrt{2}}}\right)^2\)
1/ thực hiện phép tính :a) sqrt{200}+2sqrt{108}-sqrt{98}+frac{1}{3}sqrt{frac{81}{3}}-3sqrt{75}b) (21sqrt{frac{1}{7}}+frac{1}{2}sqrt{112}-frac{14}{3}sqrt{frac{9}{7}}+7) : 3sqrt{7}c) left(sqrt{27}-sqrt{125}+sqrt{45}+sqrt{12}right).left(sqrt{75}+sqrt{20}right)d) left(frac{3}{sqrt{6}-3}-frac{3}{sqrt{6}+3}right).frac{3-sqrt{3}}{2-2sqrt{3}}-frac{sqrt{28-6sqrt{3}}}{1}e) frac{1}{sqrt{11}-2sqrt{30}}-frac{3}{sqrt{7-2sqrt{10}}}+frac{4}{sqrt{8+4sqrt{3}}}
Đọc tiếp
1/ thực hiện phép tính :
a) \(\sqrt{200}+2\sqrt{108}-\sqrt{98}+\frac{1}{3}\sqrt{\frac{81}{3}}-3\sqrt{75}\)
b) (\(21\sqrt{\frac{1}{7}}+\frac{1}{2}\sqrt{112}-\frac{14}{3}\sqrt{\frac{9}{7}}+7\)) : \(3\sqrt{7}\)
c) \(\left(\sqrt{27}-\sqrt{125}+\sqrt{45}+\sqrt{12}\right).\left(\sqrt{75}+\sqrt{20}\right)\)
d) \(\left(\frac{3}{\sqrt{6}-3}-\frac{3}{\sqrt{6}+3}\right).\frac{3-\sqrt{3}}{2-2\sqrt{3}}-\frac{\sqrt{28-6\sqrt{3}}}{1}\)
e) \(\frac{1}{\sqrt{11}-2\sqrt{30}}-\frac{3}{\sqrt{7-2\sqrt{10}}}+\frac{4}{\sqrt{8+4\sqrt{3}}}\)