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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(C=\frac{1}{4}+\frac{1}{4^2}+.....+\frac{1}{4^{1000}}\)
\(\Rightarrow4C=1+\frac{1}{4}+.....+\frac{1}{4^{1999}}\)
\(\Rightarrow4C-C=\left(1+\frac{1}{4}+.....+\frac{1}{4^{1999}}\right)-\left(\frac{1}{4}+\frac{1}{4^2}+.....+\frac{1}{4^{1000}}\right)\)
\(\Rightarrow3C=1-\frac{1}{4^{1000}}\)
\(\Rightarrow C=\frac{1}{3}-\frac{1}{3.4^{1000}}< \frac{1}{3}\)
=> C < 1 / 3
Ta có:
\(C=\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{1000}}\)
\(\Rightarrow4C=1+\frac{1}{4}+...+\frac{1}{4^{999}}\)
\(\Rightarrow4C-C=\left(1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{999}}\right)-\left(\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{999}}+\frac{1}{4^{1000}}\right)\)
\(\Rightarrow3C=1-\frac{1}{4^{1000}}\)
\(\Rightarrow C=\left(1-\frac{1}{4^{1000}}\right).\frac{1}{3}\)
\(\Rightarrow C=\frac{1}{3}-\frac{1}{4^{1000}.3}\)
Mà \(\frac{1}{3}>\frac{1}{3}-\frac{1}{4^{1000}.3}\)
\(\Rightarrow C< \frac{1}{3}\)
Vậy \(C< \frac{1}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{100}}\)
\(3A=1+\frac{1}{3}+...+\frac{1}{3^{99}}\)
\(2A=1-\frac{1}{3^{100}}\)
\(A=\frac{1-\frac{1}{3^{100}}}{2}< \frac{1-\frac{1}{3}}{2}=\frac{\frac{2}{3}}{2}=\frac{2}{3}.\frac{1}{2}=\frac{1}{3}< \frac{3}{4}\)
vậy \(\frac{1}{^{3^{100}}}\) đâu bạn
mình ko hiểu tại sao lai còn \(\frac{1}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(A=\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+.....+\frac{1}{4^{1000}}\)
\(=>4A=1+\frac{1}{4}+\frac{1}{4^2}+.....+\frac{1}{4^{999}}\)
\(=>4A-A=\left(1+\frac{1}{4}+\frac{1}{4^2}+....+\frac{1}{4^{999}}\right)-\left(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+....+\frac{1}{4^{1000}}\right)\)
\(=>3A=1-\frac{1}{4^{1000}}=>A=\frac{1-\frac{1}{4^{1000}}}{3}=\frac{1}{3}-\frac{1}{\frac{4^{1000}}{3}}<\frac{1}{3}\)
Vậy.......................
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{\sqrt{2.1}\left(\sqrt{2}+\sqrt{1}\right)}+\frac{1}{\sqrt{2.3}\left(\sqrt{3}+\sqrt{2}\right)}+\frac{1}{\sqrt{3.4}\left(\sqrt{4}+\sqrt{3}\right)}+...+\frac{1}{\sqrt{999.1000}\left(\sqrt{1000}+\sqrt{999}\right)}\)
\(A=\frac{\sqrt{2}-\sqrt{1}}{\sqrt{2.1}\left(2-1\right)}+\frac{\sqrt{3}-\sqrt{2}}{\sqrt{2.3}\left(3-2\right)}+\frac{\sqrt{4}-\sqrt{3}}{\sqrt{3.4}\left(4-3\right)}+...+\frac{\sqrt{1000}-\sqrt{999}}{\sqrt{999.1000}\left(1000-999\right)}\)
\(A=\frac{\sqrt{2}}{\sqrt{2.1}}-\frac{\sqrt{1}}{\sqrt{2.1}}+\frac{\sqrt{3}}{\sqrt{2.3}}-\frac{\sqrt{2}}{\sqrt{2.3}}+\frac{\sqrt{4}}{\sqrt{3.4}}-\frac{\sqrt{3}}{\sqrt{3.4}}+...+\frac{\sqrt{1000}}{\sqrt{999.1000}}-\frac{\sqrt{999}}{\sqrt{1000.999}}\)
\(A=\frac{1}{1}-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{3}}-\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{999}}-\frac{1}{\sqrt{1000}}\)
\(A=\frac{1}{1}-\frac{1}{\sqrt{1000}}=\frac{\sqrt{1000}-1}{\sqrt{1000}}=\frac{10\sqrt{10}-1}{10\sqrt{10}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
19 nha !!!!!!!!!! tick mình đi làm ơn để mình đủ 20 không mình bị phạt đấy
\(A=\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+...+\frac{1}{4^{1000}}\)
\(\Rightarrow4A=4\left(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+...+\frac{1}{4^{1000}}\right)\)
\(\Rightarrow4A=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{998}}+\frac{1}{4^{999}}\)
\(\Rightarrow4A-A=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{998}}+\frac{1}{4^{999}}-\frac{1}{4}-\frac{1}{4^2}-\frac{1}{4^3}-...-\frac{1}{4^{999}}-\frac{1}{4^{1000}}\)
\(\Rightarrow3A=1-\frac{1}{4^{1000}}\)
\(\Rightarrow A=\frac{1-\frac{1}{4^{1000}}}{3}\)
làm tiếp nhé ...okok