\(A=\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^{10}\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{29}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\cdot\left(5\cdot3-7\right)}=\dfrac{10-9}{15-7}=\dfrac{1}{8}\)
\(B=\dfrac{1}{2}\cdot\left(1+\dfrac{1}{1\cdot3}\right)\cdot\left(1+\dfrac{1}{2\cdot4}\right)\cdot...\cdot\left(1+\dfrac{1}{2022\cdot2024}\right)\)
\(=\dfrac{1}{2}\cdot\left(1+\dfrac{1}{2^2-1}\right)\left(1+\dfrac{1}{3^2-1}\right)\cdot...\cdot\left(1+\dfrac{1}{2023^2-1}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2^2}{\left(2-1\right)\left(2+1\right)}\cdot\dfrac{3^2}{\left(3-1\right)\left(3+1\right)}\cdot...\cdot\dfrac{2023^2}{\left(2023-1\right)\left(2023+1\right)}\)
\(=\dfrac{1}{2}\cdot\dfrac{2\cdot3\cdot4\cdot...\cdot2023}{1\cdot2\cdot3\cdot...\cdot2022}\cdot\dfrac{2\cdot3\cdot...\cdot2023}{3\cdot4\cdot...\cdot2024}\)
\(=\dfrac{1}{2}\cdot\dfrac{2023}{1}\cdot\dfrac{2}{2024}=\dfrac{1}{2024}\cdot\dfrac{2023}{1}=\dfrac{2023}{2024}\)
\(A=\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}\)
\(=\dfrac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^{10}.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6}\)
\(=\dfrac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^{10}.2^{19}.3^{19}-7.2^{29}.3^{18}}\\ =\dfrac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{29}.3^{19}-7.2^{29}.3^{18}}\\ =\dfrac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{29}.3^{18}.\left(5.3-7\right)}\\ =\dfrac{10-9}{15-7}=\dfrac{1}{8}\)
\(---\)
\(B=\dfrac{1}{2}.\left(1+\dfrac{1}{1.3}\right).\left(1+\dfrac{1}{2.4}\right).\left(1+\dfrac{1}{3.5}\right)......\left(1+\dfrac{1}{2022.2024}\right)\\ =\dfrac{1}{2}.\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}...\dfrac{2023^2}{2022.2024}\\ =\dfrac{1}{2}.\dfrac{2^2}{1.3}.\dfrac{3^2}{2.4}.\dfrac{4^2}{3.5}...\dfrac{2023^2}{2022.2024}\\ =\dfrac{1}{2}.\dfrac{\left(2.3.4...2023\right)^2}{\left(1.2.3...2022\right)\left(3.4.5...2024\right)}\\ =\dfrac{1}{2}.\dfrac{2023.2}{2024}=\dfrac{2023}{2024}\)
#$\mathtt{Toru}$
.Câu 7,8,9,10 ạ!!! mjk đag gấp
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ghi kết quả thôi ạ , k phải trình bày ạ , e cần gấp ạ !!!!!
giúp em với ạ em cần gấp ạ
giúp em với ạ em cần gấp ạ
giúp em với ạ em đang cần gấp ạ