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\(S=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{100}}\)
\(S=1+\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{100}}\right)\)
đặt \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{100}}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{99}}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\right)\)
\(A=1-\frac{1}{2^{100}}\)
thay A=\(1-\frac{1}{2^{100}}\)vào S ta có: \(S=1+1-\frac{1}{2^{100}}=2-\frac{1}{2^{100}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}+6^{11}}=\frac{2^6.2^6.3^5.3^5+2^9.3^9.2.2.2.5}{2^4.2^4.2^4.3^{12}+2^{11}.3^{11}}\)\(=\frac{2^{12}.3^{10}.5}{3^2+2^{11}.3^{11}}=\frac{2.5}{3^3}=\frac{10}{27}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1, Đặt \(A=\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
\(A=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)\(A=\frac{2^{28}\left(5.2^2.3^{18}-2.3^{20}\right)}{2^{28}\left(5.3^{19}-7.2.3^{18}\right)}\)
\(A=\frac{5.2^2.3^{18}-2.3^{20}}{5.3^{19}-7.2.3^{18}}\)\(A=\frac{3^{18}\left(5.2^2-2.3^2\right)}{3^{18}\left(5.3-7.2\right)}\)
\(A=\frac{5.2^2-2.3^2}{5.3-7.2}\)\(A=2\)
\(\frac{1}{2}S\)= \(\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+...+\frac{1}{198.200}\)
.\(2.\frac{1}{2}.S\)= \(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+...+\frac{2}{198.200}\)
S=\(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{198}-\frac{1}{200}\)
S = \(\frac{1}{4}-\frac{1}{200}\)
S = \(\frac{49}{200}\)
Kết bạn nhoa :33