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top scorer cop tại:tính nhanh:2/2*5+2/5*8+2/8*11+2/11*14+2/14*17? | Yahoo Hỏi & Đáp
có cách làm tại:Giúp tôi giải toán - Hỏi đáp, thảo luận về toán học - Học toán với OnlineMath
A = \(\dfrac{1}{2}\) x 5 + \(\dfrac{1}{5}\) x 8 + \(\dfrac{1}{8}\) x 11 + \(\dfrac{1}{14}\) x 17
A = \(\dfrac{5}{2}\) + \(\dfrac{8}{5}\) + \(\dfrac{11}{8}\) + \(\dfrac{17}{14}\)
A = \(\dfrac{700}{280}\) + \(\dfrac{448}{280}\) + \(\dfrac{385}{280}\) + \(\dfrac{340}{280}\)
\(\Rightarrow\) A = \(\dfrac{1873}{280}\)
A \(=\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+\dfrac{1}{11.14}+\dfrac{1}{14.17}\)
A \(=\)\(\dfrac{1}{3}\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17}\right)\)
A \(=\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}\right)\)
A \(=\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{17}\right)\)
A \(=\dfrac{1}{3}.\dfrac{15}{34}\)
A \(=\dfrac{5}{34}\)
\(\left(32^8.11-32^3.32^5\right):32^7\)
\(=\left(32^8.11-32^8\right):32^7\)
\(=\left[32^8.\left(11-1\right)\right]:32^7\)
\(=\left[32^8.10\right]:32^7\)
\(=\frac{32^8}{32^7}.\frac{10}{32^7}\)
\(=\frac{32.10}{32^7}\)
\(=\frac{10}{32^6}\)
\(E=\frac{3^2}{8.11}+\frac{3^2}{11.14}+......+\frac{3^2}{197.200}\)
\(E=3.\left(\frac{3}{8.11}+\frac{3}{11.14}+......+\frac{3}{197.200}\right)\)
\(E=3.\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+.....+\frac{1}{197}-\frac{1}{200}\right)\)
\(E=3.\left(\frac{1}{8}-\frac{1}{200}\right)\)
\(E=3.\frac{3}{25}\)
\(E=\frac{9}{25}\)
\(\frac{1}{3}E=\frac{3}{8x11}+\frac{3}{11x14}+..+\frac{3}{197x200}\)
\(\frac{1}{3}E=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+.+\frac{1}{197}-\frac{1}{200}\)
\(\frac{1}{3}E=\frac{1}{8}-\frac{1}{200}\)
\(\frac{1}{3}E=\frac{3}{25}\)
\(E=\frac{9}{25}\)