Đề bài: Tính nhanh:
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c) \(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}=\dfrac{1}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\right)\)
\(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{13}\right)=\dfrac{1}{2}.\dfrac{10}{39}=\dfrac{5}{39}\)
e) \(\dfrac{1}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{1}{5}-\dfrac{1}{5}=\dfrac{1}{5}\left(\dfrac{4}{7}+\dfrac{3}{7}\right)-\dfrac{1}{5}=\dfrac{1}{5}.1-\dfrac{1}{5}=0\)
b: \(=\dfrac{1}{9}\cdot\dfrac{3}{5}+\dfrac{5}{6}\cdot\dfrac{3}{5}-\dfrac{7}{2}\cdot\dfrac{3}{5}\)
\(=\dfrac{3}{5}\left(\dfrac{1}{9}+\dfrac{5}{6}-\dfrac{7}{2}\right)=\dfrac{3}{5}\cdot\dfrac{-23}{9}=\dfrac{-69}{45}=\dfrac{-23}{15}\)
d: \(=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(-\dfrac{20}{41}-\dfrac{21}{41}\right)-\dfrac{5}{7}=-\dfrac{5}{7}\)
15.37.4 + 120.21 + 21.5.12 = 15.4.37 + 21.2.60 + 5.12.21 = 60.37 + 42.60 + 60.21 = 60.(37 + 42 + 21) = 60.100 = 6000
7,1 + 7,2 + 7,3 + 7,4 + ... + 7,9
= ( 7,1 + 7,9 ) + ( 7,2 + 7,8 ) + ( 7,3 + 7,7 ) + ( 7,4 + 7,6 ) + 7,5
= 15 + 15 + 15 + 15 + 7,5
= 15 x 4 + 7,5
= 60 + 7,5
= 67,5
\(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}\left(6-1\right)}\)
\(=\frac{2.6}{3.5}=\frac{4}{5}\)
= 4/5 nha bạn