Mờ wá!

\(A=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}.....\dfrac{99}{100}\)

\(\Leftrightarrow A=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.\dfrac{4.6}{5.5}.....\dfrac{9.11}{10.10}\)

\(=\dfrac{1.3.2.4.3.5.4.6....9.11}{2.2.3.3.4.4.5.5.....10.10}\)

\(=\dfrac{\left(1.2.3.4.5....9\right).\left(2.3.4.5.6.....11\right)}{\left(2.3.4.5.6.....10\right)\left(2.3.4.5.6.....10\right)}\)

\(=\dfrac{11}{10}\)

\(D=\dfrac{4^6.9^5+6^9.120}{-8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+3^9.2^9.2^3.3.5}{-2^{12}.3^{12}-2^{11}.3^{11}}\\ =\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-6^{12}-6^{11}}=\dfrac{2^{12}.3^{10}\left(1+5\right)}{6^{11}\left(-6-1\right)}=\dfrac{2^{12}.3^{10}.6}{6^{11}.-7}=\dfrac{2^{12}.3^{10}.2.3}{6^{11}.-7}\\ =\dfrac{2^{13}.3^{11}}{6^{11}.-7}=\dfrac{2^{11}.3^{11}.2^2}{6^{11}.-7}=\dfrac{6^{11}.4}{6^{11}.-7}=-\dfrac{4}{7}\)

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