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\(A=\frac{15.3^{11}+4.27^1}{9^7}\)
\(\Rightarrow A=\frac{3.5.3^{11}+4.3^{3^1}}{\left(3^2\right)^7}\)
\(\Rightarrow A=\frac{3^{12}.5+4.3^3}{3^{14}}\)
\(\Rightarrow A=\frac{3^3.\left(5.3^8+4.3^3\right)}{3^{14}}\)
\(\Rightarrow A=\frac{32805+4}{177147}\)
\(\Rightarrow A=\frac{32809}{177147}\)
Đặt \(A=\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
\(A=\frac{2^{19}\cdot\left(3^3\right)^3+15\cdot\left(2^2\right)^9\cdot\left(3^2\right)^4}{6^9\cdot2^9\cdot2+12^{10}}\)
\(A=\frac{2^{19}\cdot3^9+15\cdot2^{18}\cdot3^8}{12^9\cdot2+12^9\cdot12}=\frac{\left(2^{18}\cdot3^8\right)\cdot6+\left(2^{18}\cdot3^8\right)\cdot15}{12^9\cdot\left(2+12\right)}\)
\(A=\frac{\left(2^{18}\cdot3^8\right)\cdot\left(6+15\right)}{12^9\cdot14}=\frac{2^{18}\cdot3^8\cdot21}{12^9\cdot14}=\frac{2^{18}\cdot3^8\cdot7\cdot3}{2^{18}\cdot3^9\cdot7\cdot2}=\frac{3^8\cdot3}{3^8\cdot3\cdot2}\)
\(A=\frac{1}{2}\)
Đặt \(B=\frac{4}{35}+\frac{4}{63}+\frac{4}{99}+\frac{4}{143}+\frac{4}{195}=\frac{4}{5\cdot7}+\frac{4}{7\cdot9}+\frac{4}{9\cdot11}+\frac{4}{11\cdot13}+\frac{4}{13\cdot15}\)
\(B=\frac{1}{2}\left(\frac{4}{5}-\frac{4}{7}+\frac{4}{7}-\frac{4}{9}+...+\frac{4}{13}-\frac{4}{15}\right)\)
\(B=\frac{1}{2}\left(\frac{4}{5}-\frac{4}{15}\right)\)mà \(\frac{4}{5}-\frac{4}{15}< 1\Leftrightarrow\frac{1}{2}\left(\frac{4}{5}-\frac{4}{15}\right)< \frac{1}{2}\Leftrightarrow B< A\)
Câu 1 : \(1,321338308x10^{-4}\)
Câu 2 : \(1316,572106\)
Câu 3 : \(1,641302619x10^{-13}\)
Ủng hộ nhé,tớ đang âm.