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\(\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\times\left(1-\frac{1}{7}\right)\times\left(1-\frac{1}{8}\right)-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{8}-\frac{1}{4}\times\frac{1}{2}\)
\(=\frac{2}{8}-\frac{1}{8}=\frac{1}{8}\)
\(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{6}\times\frac{15}{4}\)
\(=\frac{6}{5}\times\frac{2}{6}\times\frac{15}{4}\)
\(=\frac{2}{5}\times\frac{15}{4}\)
\(=\frac{3}{2}\)
Ta có: \(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)
\(=2.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2.\left(1-\frac{1}{20}\right)=\frac{2.19}{20}=\frac{19}{10}\)
\(\frac{2}{1\times2}+\frac{2}{2\times3}+......+\frac{2}{19\times20}\)
\(=2\left(\frac{1}{1\times2}+\frac{1}{2\times3}+.......+\frac{1}{19\times20}\right)\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+........+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2\left(1-\frac{1}{20}\right)=2.\frac{19}{20}=\frac{19}{10}\)
\(\frac{1}{2}+\frac{2}{3}+\frac{3}{5}=\frac{3}{6}+\frac{4}{6}+\frac{3}{5}\)
=\(\frac{7}{6}+\frac{3}{5}\)
\(=\frac{35}{30}+\frac{18}{30}=\frac{53}{30}\)
\(\frac{3}{8}+\frac{3}{4}+\frac{1}{16}=\frac{6}{16}+\frac{12}{16}+\frac{1}{16}\)
=\(\frac{18}{16}+\frac{1}{16}\)
\(=\frac{19}{16}\)
b) 1/3+1/3^2+1/3^3+1/3^4+1/3^5 (goi tong bang M)
3M=1+1/3+1/3^2+1/3^3+1/3^4
3M-M=1-1/3^5
2M=242/243
M=242/243*1/2=121/243
\(\frac{12}{20}\)= \(\frac{6}{10}\)= \(\frac{3}{5}\)
\(\frac{3}{4}\)= \(\frac{9}{12}\)= \(\frac{12}{16}\)= \(\frac{15}{20}\)
\(\frac{75}{45}\)= \(\frac{15}{9}\)= \(\frac{5}{3}\)
\(\frac{3}{4}\)= \(\frac{18}{24}\)= \(\frac{12}{16}\)
12/20 = 6/10 = 3/5
3/4 = 9/12 = 12/16 = 15/20
75/45 = 15/9 = 5/3
3/4 = 18/24 = 12/16
Tk mk nha
12/14 + 15/20 + 6/7 + 3/4
= ( 12/14 + 6/7 ) + ( 15/20 + 3/4 )
= ( 6/7 + 6/7 ) + ( 3/4 + 3/4 )
= 12/7 + 6/4
= 48/28 + 42/28
= 90/28
= 45/14
Tham khảo nha !!!
4/12=2/6=1/3