CMR\(\frac{1}{2\sqrt{n+1}}< \sqrt{n+1}-\sqrt{n}\)với n thuộc N
Áp dụng CMR \(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{2500}}< 100\)
Những câu hỏi liên quan
CMR \(\frac{1}{2\sqrt{n+1}}
CMR \(2\left(\sqrt{n+1}-\sqrt{n}\right)< \frac{1}{\sqrt{n}}< 2\left(\sqrt{n}-\sqrt{n-1}\right)\)với n thuộc N*
Áp dụng cho S=\(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{100}}\)
CMR 18<S<19
CMR:
Với n thuộc N*
\(a)1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}>\sqrt{n}\\ b)\frac{1}{\sqrt{n}}>2\left(\sqrt{n-1}-\sqrt{n}\right)\)
cmr với mọi n thuộc N* \(1+\frac{1}{2\sqrt{2}}+\frac{1}{3\sqrt{3}}+...+\frac{1}{n\sqrt{n}}< 2\sqrt{2}\)
1) CMR frac{1}{sqrt{1.1999}}+frac{1}{sqrt{2.1998}}+frac{1}{sqrt{3.1997}}+...+frac{1}{sqrt{1999.1}}ge1,9992) CMR frac{1}{1sqrt{2}+2sqrt{1}}+frac{1}{3sqrt{2}+2sqrt{3}}+...+frac{1}{95sqrt{94}+94sqrt{95}} 13) CMR frac{1}{2sqrt{1}}+frac{1}{3sqrt{2}}+frac{1}{4sqrt{3}}+...+frac{1}{left(n+1right)sqrt{n}} 24) CMR sqrt{n} frac{1}{sqrt{1}}+frac{1}{sqrt{2}}+frac{1}{sqrt{3}}+...+frac{1}{sqrt{n}} 2sqrt{n}
Đọc tiếp
1) CMR \(\frac{1}{\sqrt{1.1999}}+\frac{1}{\sqrt{2.1998}}+\frac{1}{\sqrt{3.1997}}+...+\frac{1}{\sqrt{1999.1}}\ge1,999\)
2) CMR \(\frac{1}{1\sqrt{2}+2\sqrt{1}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{95\sqrt{94}+94\sqrt{95}}< 1\)
3) CMR \(\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+...+\frac{1}{\left(n+1\right)\sqrt{n}}< 2\)
4) CMR \(\sqrt{n}< \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}< 2\sqrt{n}\)
\(2\left(\sqrt{N+1}-\sqrt{N}\right)<\frac{1}{\sqrt{N}}<2\left(\sqrt{N}-\sqrt{N-1}\right)\)
Với N>0
Áp dụng: cho s=\(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{100}}\)
Cmr 18<s<19
Bài 1: CMR
Bài 2: CMR
1, CMR: \(1+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{n^2}\ge\frac{n}{n+1}\)
2, CMR: \(2\left(\sqrt{n-1}-1\right)< 1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}\)
3, CMR: \(\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+...+\frac{1}{\left(n+1\right)\sqrt{n}}< 2\)
cho A=\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+....+\frac{1}{\sqrt{n^2}}\)
với n thuộc N , n>=2
cmr; A không phải là số tự nhiên