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\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}\)
\(=\frac{101\left(14+15+16+17+18+19\right)}{101\left(20+21+22+23+24+25\right)}\)
\(=\frac{\left(19+14\right)\left(19-14+1\right):2}{\left(25+20\right)\left(25-20+1\right):2}\)
=\(\frac{33.6:2}{45.6:2}=\frac{33}{45}=\frac{11}{15}\)
\(a-68=\left(3\frac{10}{11}-4\right):\left(\frac{2121}{2222}-1\right):\left(\frac{33333}{343434}-1\right)\)
\(a-68=\left(\frac{43}{11}-4\right):\left(\frac{-1}{22}\right):\left(\frac{-310101}{343434}\right)\)
\(a-68=\frac{-1}{11}.\frac{-22}{1}.\frac{-343434}{310101}\)
\(a-68=\frac{1}{11}.\frac{22}{1}.\frac{343434}{310101}.\left(-1\right)\)
\(a-68=\frac{-686868}{310101}\)
\(a=\frac{-686868}{310101}+68\)
\(a=\frac{-20400000}{310101}\)
Vậy \(a=\frac{-20400000}{310101}\)
Ta có:2222 chia 7 dư 3
=>2222 đồng dư với -4(mod 7)
=>2222-(-4) chia hết cho 7
=>2226 chia hết cho 7
=>đpcm
Ta thấy : \(2222^{3333}vs2^{300}:\hept{\begin{cases}2222>2\\3333>300\end{cases}\Rightarrow2222^{3333}>2^{300}}\)
Ta thấy : \(2222^{1111}=1111^{1111}.2^{1111}< 1111^{1111}.1111^{1110}=1111^{2221}\)
Ta thấy : \(54^{10}=\left(3^3\right)^{10}.2^{10}=3^{30}.2^{10}=3^{12}.3^{18}.2^{10}>3^{12}.7^{12}=21^{12}.\)
1414+1515+1616+1717+1818+1919/2020+2121+2222+2323+2424+2525
=14.101+15.101+16.101+17.101+18.101+19.101/20.101+21.101+22.101+23.101+24.101+25.101
=14+15+16+17+18+19/20+21+22+23+24+25
=99/135
=11/15
1414+1515+1616+1717+1818+1919/2020+2021+2222+2323+2424+2525
=14.101+15.101+16.101+17.101+18.101+19.101/20.101+21.101+22.101+23.101+24.101+25.101
=14+15+16+17+18+19/20+21+22+23+24+25
=99/135
=11/15
