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Câu hỏi của Vũ Thảo Vy - Toán lớp 9 - Học toán với OnlineMath
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Tính \(S=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\)\(\frac{1}{25\sqrt{24}+24\sqrt{25}}\)
CMR:
\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{25\sqrt{24}+24\sqrt{25}}< 1\)
CMR
\(\sqrt{n}< \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+........+\frac{1}{\sqrt{n}}< 2\sqrt{n}\)
\(\sqrt{1}+\sqrt{2}+.......+\sqrt{n}< n\sqrt{\frac{n+1}{2}}\)
\(\frac{\sqrt{2}-\sqrt{1}}{1+2}+\frac{\sqrt{3}-\sqrt{2}}{2+3}+.........+\frac{\sqrt{25}-\sqrt{24}}{24+25}< \frac{2}{5}\)
\(A=\frac{\sqrt{2}-\sqrt{1}}{2+1}+\frac{\sqrt{3}-\sqrt{2}}{3+2}+...+\frac{\sqrt{25}+\sqrt{24}}{25+24}\)
CMR A<0,4
Tính A=\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{24}+\sqrt{25}}\)
a) CMR: \(\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n-1}}\) với \(n\in N\)*
b) tính \(B=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+......+\frac{1}{25\sqrt{24}+24\sqrt{25}}\)
Bt: Tính
a) \(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{25\sqrt{24}+24\sqrt{25}}\)
b) C/m: \(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}\)
c) C/m: \(\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+...+\frac{1}{\left(n+1\right)\sqrt{n}}
Bt: Tính a) frac{1}{2sqrt{1}+1sqrt{2}}+frac{1}{3sqrt{2}+2sqrt{3}}+...+frac{1}{25sqrt{24}+24sqrt{25}}b) C/m: frac{1}{2sqrt{1}+1sqrt{2}}+frac{1}{3sqrt{2}+2sqrt{3}}+...+frac{1}{left(n+1right)sqrt{n}+nsqrt{n+1}}c) C/m: frac{1}{2sqrt{1}}+frac{1}{3sqrt{2}}+frac{1}{4sqrt{3}}+...+frac{1}{left(n+1right)sqrt{n}}2d) C/m: sqrt{n}frac{1}{sqrt{1}}+frac{1}{sqrt{2}}+frac{1}{sqrt{3}}+...+frac{1}{sqrt{n}}2sqrt{n}
Đọc tiếp
Bt: Tính
a) \(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{25\sqrt{24}+24\sqrt{25}}\)
b) C/m: \(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}\)
c) C/m: \(\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+...+\frac{1}{\left(n+1\right)\sqrt{n}}<2\)
d) C/m: \(\sqrt{n}<\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}<2\sqrt{n}\)
rút gọn:\(\frac{1}{\sqrt{1}-\sqrt{2}}+\frac{1}{\sqrt{2}-\sqrt{3}}+...+\frac{1}{\sqrt{24}-\sqrt{25}}\)