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A = \(\dfrac{5}{9}\cdot\left(\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{3}{7}\right)\)
=\(\dfrac{5}{9}\cdot\dfrac{5}{7}=\dfrac{25}{63}\)
\(\frac{3^8.5^9+15^8.3^2}{15^9.3^3-3^8.5^9}\)
\(=\frac{3^8.5^9+5^8.3^{10}}{5^9.3^{12}-3^8.5^9}\)
\(=\frac{3^8.5^8.\left(5+3^2\right)}{5^9.3^8.\left(3^4-1\right)}=\frac{14}{80}=\frac{7}{40}\)
\(=\frac{15^8.5+15^8.3^2}{15^8.5.3.3^3-15^8.5}\)
\(=\frac{15^8\left(5+9\right)}{15^8\left(5.3^4-5\right)}\)
\(=\frac{15^8.14}{15^8.400}\)
\(=\frac{14}{400}\)
\(=\frac{7}{200}\)
a) \(\left(-3\right)\cdot\left(-2\right)\cdot\left(-5\right)\cdot4=-120\)
Ta có:
\(A=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...+\frac{100}{3^{100}}\)
\(\Rightarrow3A=1+\frac{2}{3}+\frac{3}{3^2}+\frac{4}{3^3}+...+\frac{100}{3^{99}}\)
\(\Rightarrow2A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{99}}-\frac{100}{3^{100}}\)
\(\Rightarrow6A=3+1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{98}}-\frac{100}{3^{99}}\)
\(\Rightarrow4A=3-\frac{101}{3^{99}}+\frac{100}{3^{100}}=3-\frac{203}{3^{100}}\)
\(\Rightarrow A=\frac{3-\frac{203}{3^{100}}}{4}=\frac{3}{4}-\frac{203}{3^{100}.4}< \frac{3}{4}\Rightarrowđpcm\)
Vậy \(A< \frac{3}{4}\)
58.2417353404 nha bn !
hok tốt thi tốt
=9.31+9.9-40.9
=9.(31+9-40)
=9.0
=0