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\(A=\frac{5-2}{2x5}+\frac{8-5}{5x8}+\frac{11-8}{8x11}+...+\frac{20-17}{17x20}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\)
\(A=\frac{1}{2}-\frac{1}{20}=\frac{9}{20}\)
Đặt \(A=\frac{240\cdot50+48\cdot50}{42\cdot37+21\cdot126}=\frac{48\cdot5\cdot50+48\cdot50}{21\cdot2\cdot37+21\cdot126}\)
\(\Rightarrow A=\frac{48\cdot250+48\cdot50}{21\cdot74+21\cdot126}=\frac{48\cdot\left(250+50\right)}{21\cdot\left(74+126\right)}\)
\(\Rightarrow A=\frac{48\cdot300}{21\cdot300}=\frac{48}{21}=\frac{16}{7}\)
\(\frac{2}{3}+\frac{2007}{2009}+\frac{4}{3}-1\)
\(=\frac{2}{3}+\frac{4}{3}+\frac{2007}{2009}-1\)
\(=2+\frac{-2}{2009}\)
\(=\frac{4018}{2009}-\frac{2}{2009}\)
\(=\frac{4016}{2009}\)
Học tốt
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{56}=\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}...\frac{1}{7x8}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\)\(-\frac{1}{8}=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)
b,
Ta có : \(\frac{1919}{2323}x\frac{464646}{747474}x\frac{37}{19}\)
\(=\frac{19}{23}x\frac{23}{37}x\frac{37}{19}\)
\(=\frac{19x23x37}{23x37x19}\)
\(=1\)
~ Chúc các bn học giỏi và may mắn ~
\(\frac{1919}{2323}.\frac{464646}{747474}.\frac{37}{19}\)
\(=\frac{1919:101}{2323:101}.\frac{464646:10101}{747474:10101}.\frac{37}{19}\)
\(=\frac{19}{23}.\frac{46}{74}.\frac{37}{19}\)
\(=\frac{19.46.37}{23.74.19}=\frac{19.23.2.37}{23.37.2.19}=1\)
\(\frac{3}{7}+\frac{4}{5}+\frac{4}{7}=\left(\frac{3}{7}+\frac{4}{7}\right)+\frac{4}{5}=1+\frac{4}{5}=\frac{9}{5}\)
\(\frac{6}{11}+\frac{1}{3}+\frac{5}{11}=\left(\frac{6}{11}+\frac{5}{11}\right)+\frac{1}{3}=1+\frac{1}{3}=\frac{4}{3}\)
a) \(\frac{3}{7}+\frac{4}{5}+\frac{4}{7}\)
= \(\left(\frac{3}{7}+\frac{4}{7}\right)+\frac{4}{5}\)
= \(1+\frac{4}{5}\)
= \(\frac{9}{5}\)
b) \(\frac{6}{11}+\frac{1}{3}+\frac{5}{11}\)
= \(\left(\frac{6}{11}+\frac{5}{11}\right)+\frac{1}{3}\)
= \(1+\frac{1}{3}\)
= \(\frac{4}{3}\)
= (8x125)x(50x2)x(45x10+45)
= 1000x100x495
= 49.500.000
\(=\frac{3}{4}\left(\frac{8}{9}+\frac{2}{3}\right)=\frac{3}{4}\left(\frac{8}{9}+\frac{6}{9}\right)=\frac{3}{4}x\frac{14}{9}=\frac{7}{6}..\)
mình nhầm chỗ \(\frac{8}{9}\)và \(\frac{3}{4}\)có một dấu cộng
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