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22 tháng 7 2017
E = \(\frac{36}{1\cdot7}+\frac{36}{7\cdot13}+...+\frac{36}{94\cdot100}=\frac{36}{6}\left[\frac{1}{1\cdot7}+\frac{1}{7\cdot13}+...+\frac{1}{94\cdot100}\right]\)
\(=6\left[1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{94}-\frac{1}{100}\right]=6\left[1-\frac{1}{100}\right]\)
\(=6\cdot\frac{99}{100}=\frac{297}{50}\)
F = \(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+...+\frac{1}{\left[3a+2\right]\left[3a+5\right]}\)
\(=\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{\left[3a+2\right]\left[3a+5\right]}\)
\(=\frac{1}{3}\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{3a+2}-\frac{1}{3a+5}\right]\)
\(=\frac{1}{3}\left[\frac{1}{2}-\frac{1}{3a+5}\right]=\frac{1}{6}-\frac{1}{9a+15}\)
G = \(\frac{1}{2\cdot3}+\frac{2}{3\cdot5}+\frac{3}{5\cdot8}+\frac{4}{8\cdot12}+\frac{5}{12\cdot17}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{12}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
1 tháng 2 2022
a: \(=\left(1.25\right)^{16}\cdot8^{16}\cdot8=8\cdot10^{16}\)
b: \(=\left(\dfrac{5}{2}\right)^{13}\cdot4^{13}\cdot4^2=10^{13}\cdot4^2\)
c: \(=\left(0.25\right)^4\cdot8^4\cdot8^2=2^4\cdot8^2=64\cdot16=1024\)
d: \(=\left(\dfrac{1}{2}\right)^{15}\cdot2^{18}=2^3=8\)
e: \(=\left(\dfrac{1}{3}\cdot6\right)^7\cdot\left(\dfrac{1}{2}\right)^7\cdot\dfrac{1}{2}=2^7\cdot\left(\dfrac{1}{2}\right)^7\cdot\dfrac{1}{2}=\dfrac{1}{2}\)
7 tháng 4 2020
a) \(\frac{2^7\cdot9^3}{6^5\cdot8^2}=\frac{2^7\cdot\left(3^2\right)^3}{\left(2\cdot3\right)^5\cdot\left(2^3\right)^2}=\frac{2^7\cdot3^6}{2^5\cdot3^5\cdot2^6}=\frac{3}{2^4}=\frac{3}{16}\)
c) \(\frac{5^4\cdot20^4}{25^4\cdot4^5}=\frac{5^4\cdot\left(2^2\cdot5\right)^4}{\left(5^2\right)^4\cdot\left(2^2\right)^5}=\frac{5^4\cdot2^8\cdot5^4}{5^8\cdot2^{10}}=\frac{1}{2^2}=\frac{1}{4}\)
d) \(\frac{\left(5^4\cdot20^4\right)^3}{125^4}=\frac{5^{12}\cdot20^{12}}{\left(5^3\right)^4}=\frac{5^{12}\cdot\left(2^2\cdot5\right)^{12}}{5^{12}}=2^{24}\cdot5^{12}\)
29 tháng 11 2016
a)\(\left(-3\right)^{x+3}=-\frac{1}{27}\)
\(\left(-3\right)^{x+3}=\left(-\frac{1}{3}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-\frac{3^0}{3^1}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-3^{-1}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-3\right)^{-3}\)
\(\Rightarrow x+3=-3\)
\(\Rightarrow x=-6\)
b)\(\left(-6\right)^{2x+2}=\frac{1}{36}\)
\(\left(-6\right)^{2x+2}=\left(-\frac{1}{6}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-\frac{6^0}{6^1}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-6^{-1}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-6\right)^{-2}\)
\(\Rightarrow2x+2=-2\)
\(\Rightarrow2x=-4\)
\(\Rightarrow x=-2\)
c)\(\left(-3\right)^{x+5}=\frac{1}{81}\)
\(\left(-3\right)^{x+5}=\left(-\frac{1}{3}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-\frac{3^0}{3^1}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-3^{-1}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-3\right)^{-4}\)
\(\Rightarrow x+5=-4\)
\(\Rightarrow x=-9\)
29 tháng 11 2016
d)\(\left(\frac{1}{9}\right)^x=\left(\frac{1}{27}\right)^6\)
\(\left[\left(\frac{1}{3}\right)^2\right]^x=\left[\left(\frac{1}{3}\right)^3\right]^6\)
\(\left(\frac{1}{3}\right)^{2x}=\left(\frac{1}{3}\right)^{18}\)
\(\Rightarrow2x=18\)
\(\Rightarrow x=9\)
e)\(\left(\frac{4}{9}\right)^x=\left(\frac{8}{27}\right)^6\)
\(\left[\left(\frac{2}{3}\right)^2\right]^x=\left[\left(\frac{2}{3}\right)^3\right]^6\)
\(\left(\frac{2}{3}\right)^{2x}=\left(\frac{2}{3}\right)^{18}\)
\(\Rightarrow2x=18\)
\(\Rightarrow x=9\)
\(C=\frac{1}{2.3}+\frac{2}{3.5}+\frac{3}{5.8}+\frac{4}{8.12}+\frac{2,5}{6.17}+\frac{6}{17.23}+\frac{3,5}{15.23}\)
\(=\frac{1}{2.3}+\frac{2}{3.5}+\frac{3}{5.8}+\frac{4}{8.12}+\frac{5}{12.17}+\frac{6}{17.23}+\frac{7}{23.30}\)
\(=\frac{3-2}{2.3}+\frac{5-3}{3.5}+\frac{8-5}{5.8}+\frac{12-8}{8.12}+\frac{17-12}{12.17}+\frac{23-17}{17.23}+\frac{30-23}{23.30}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{23}+\frac{1}{23}-\frac{1}{30}\)
\(=\frac{1}{2}-\frac{1}{30}=\frac{7}{15}\)