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\(\frac{12}{7}\times\frac{2}{11}+\frac{12}{11}\times\frac{15}{7}-\frac{12}{7}\times\frac{6}{11}\)
\(=\frac{12}{7}\times\frac{2}{11}+\frac{12}{7}\times\frac{15}{11}-\frac{12}{7}\times\frac{6}{11}\)
\(=\frac{12}{7}\times\left(\frac{2}{11}+\frac{15}{11}-\frac{6}{11}\right)\)
\(=\frac{12}{7}\times1=\frac{12}{7}\)
\(\frac{12}{7}.\frac{2}{11}+\frac{12}{11}.\frac{15}{7}-\frac{12}{7}.\frac{6}{11}\)
= \(\frac{24}{77}\)+\(\frac{180}{77}\)-\(\frac{72}{77}\)
=\(\frac{132}{77}\)
\(A=\frac{15\times3^{11}+4\times27^4}{9^7}\)
\(A=\frac{15\times177147+4\times531441}{4782969}\)
\(A=\frac{2657205+2125764}{4782969}\)
\(A=\frac{47829969}{47829969}=1\)
=\(\frac{3\left(\frac{1}{1}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{2}{4}+\frac{2}{6}+\frac{2}{8}}{5\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}\)
=\(\frac{3}{5}+\frac{2\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}{5\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}\)=\(\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\)
Ta có : \(\frac{\frac{3}{5}+\frac{3}{7}-\frac{1}{3}+\frac{3}{11}}{\frac{6}{5}+\frac{6}{7}-\frac{2}{3}+\frac{6}{11}}=\frac{\frac{3}{5}+\frac{3}{7}-\frac{1}{3}+\frac{3}{11}}{2\left(\frac{3}{5}+\frac{3}{7}-\frac{1}{3}+\frac{3}{11}\right)}=\frac{1}{2}\)
Lại có : \(\frac{\left(\frac{1}{4}-\frac{1}{5}-\frac{1}{20}\right).2021}{\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}}=\frac{0.2021}{\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}}=0\)
Khi đó \(B=\frac{1}{2}+0=\frac{1}{2}\)
\(\frac{5}{6}+6\frac{1}{6}.\left(11\frac{94}{1591}-6\frac{38}{1951}\right):8\frac{11}{43}\)
= \(\frac{5}{6}+\frac{37}{6}.\frac{8011}{1591}:8\frac{11}{43}\)
= \(\frac{5}{6}+\frac{8011}{258}:\frac{355}{43}\)
= \(\frac{5}{6}+\frac{344473}{91590}\)
= \(\frac{1631}{355}\)
Ta có: A=1/11+1/12+1/13+...+1/30
=(1/11+1/12+1/13+..+1/20)+(1/21+1/22+1/23+...+1/30)
\(\Rightarrow\)A<(1/10+1/10+1/10+...+1/10)+(1/20+1/20+1/20+...1/20)
\(\Rightarrow\)A<(1/10)*10+(1/20)*10
\(\Rightarrow\)A<1+1/2
\(\Rightarrow\)A<3/2<11/6
\(11M=\frac{11^6+11}{11^6+1}=\frac{11^6+1+10}{11^6+1}=\frac{11^6+1}{11^6+1}+\frac{10}{11^6+1}=1+\frac{10}{11^6+1}\)
\(11N=\frac{11^7+11}{11^7+1}=\frac{11^7+1+10}{11^7+1}=\frac{11^7+1}{11^7+1}+\frac{10}{11^7+1}=1+\frac{10}{11^7+1}\)
vì \(\frac{10}{11^6+1}>\frac{10}{11^7+1}\)
nên\(11M>11N\)
=>\(M>N\)
\(M=\frac{11^5+1}{11^6+1}\)
\(\Rightarrow11M=11.\frac{11^5+1}{11^6+1}=\frac{11^6+11}{11^6+1}=\frac{11^6+1+10}{11^6+1}=1+\frac{10}{11^6+1}\)
\(N=\frac{11^6+1}{11^7+1}\)
\(\Rightarrow11N=11.\frac{11^6+1}{11^7+1}=\frac{11^7+11}{11^7+1}=\frac{11^7+1+10}{11^7+1}=1+\frac{10}{11^7+1}\)
Do \(1+\frac{10}{11^6+1}>1+\frac{10}{11^7+1}\)
\(\Rightarrow11M>11N\)
\(\Rightarrow M>N\)