\(\frac{1010+1111+1212+1313+1414+1515+1616+1717}{2020+2121+2222+2323+2424+2525+2626+2727}\)

\(=\frac{101.10+101.11+...+101.17}{101.20+101.21+...+101.27}\)

\(=\frac{101.\left(10+11+...+17\right)}{101.\left(20+21+...+27\right)}\)

\(=\frac{108}{188}\)

\(=\frac{27}{47}\)

\(2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right)\cdot5.y>\frac{5}{6}\)

\(\Rightarrow2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right):5.y>\frac{5}{6}\)

\(\Rightarrow2>\left(\frac{20}{120}+\frac{16}{120}+\frac{9}{120}+\frac{5}{120}\right):5.y>\frac{5}{6}\)

\(\Rightarrow2>\frac{5}{12}:5.y>\frac{5}{6}\)

\(\Rightarrow2>\frac{1}{12}.y>\frac{5}{6}\)

Đặt :\(\frac{1}{12}.y=2\Rightarrow y=2:\frac{1}{12}=24\)

\(\frac{1}{12}.y=\frac{5}{6}\Rightarrow y=\frac{5}{6}:\frac{1}{12}=10\)

\(\Rightarrow24>y>10\)

\(\Rightarrow y\in\left\{11;12;...;23\right\}\)

ko biết

I am sorry

Kb nhé

Ai làm đúng và nhanh nhất mk k cho

cái thứ hai lớn hơn

Ta có : \(\frac{1212+1313+1414+1515+1616}{1717+1818+1919+2020+2121}=\frac{12+13+14+15+16}{17+18+19+20+21}=\frac{28\cdot\frac{5}{2}}{38\cdot\frac{5}{2}}=\frac{14}{19}\)

Dễ thấy \(\frac{111111}{666665}< \frac{1}{2}\) ( do 111111 < 666665/2 ) và \(\frac{14}{19}>\frac{1}{2}\) ( do 14 > 19/2 )

Vậy \(\frac{111111}{666665}< \frac{1212+1313+1414+1515+1616}{1717+1818+1919+2020+2121}\)

Ta có: \(\frac{\frac{3}{7}-\frac{3}{17}+\frac{3}{171}-\frac{3}{1717}}{\frac{9}{7}-\frac{9}{17}+\frac{9}{171}-\frac{9}{1717}}\)= \(\frac{3.\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{171}-\frac{1}{1717}\right)}{9.\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{171}-\frac{1}{1717}\right)}\)=\(\frac{3}{9}=\frac{1}{3}\)

= 1x1x1

=1

\(\left(\frac{151515}{161616}+\frac{17^9}{17^{10}}\right)-\left(\frac{1500}{1600}-\frac{1616}{1717}\right)\)

\(=\left(\frac{15}{16}+\frac{1}{17}\right)-\left(\frac{15}{16}-\frac{16}{17}\right)\)

\(=\frac{15}{16}+\frac{1}{17}-\frac{15}{16}+\frac{16}{17}\)

\(=\left(\frac{15}{16}-\frac{15}{16}\right)+\left(\frac{1}{17}+\frac{16}{17}\right)\)

\(=\frac{15-15}{16}+\frac{1+16}{17}\)

\(=0+\frac{17}{17}\)

\(=0+1\)

\(=1\)

thank

\(S=\left(\frac{17}{71}+\frac{17.101}{71.101}+\frac{17.10101}{71.10101}\right):\frac{17.1010101}{71.1010101}\)

\(S=\left(\frac{17}{71}+\frac{17}{71}+\frac{17}{71}\right):\frac{17}{71}\)

\(S=3.\frac{17}{71}:\frac{17}{71}=3\)

\(S=\left(\frac{17}{71}+\frac{17.101}{71.101}+\frac{17.10101}{71.10101}\right):\frac{17.1010101}{71.1010101}\)

\(S=\left(\frac{17}{71}+\frac{17}{71}+\frac{17}{71}\right):\frac{17}{71}\)

\(S=3.\frac{17}{71}:\frac{17}{71}\)

\(\Rightarrow S=3\)

Rất vui vì giúp đc bạn <3

=\(\left(\frac{15}{16}+\frac{1}{17^5}\right)+\left(\frac{16}{17}-\frac{15}{16}\right)\)

=\(\frac{1}{17^5}+\frac{16}{17}=\frac{1+16.17^4}{17^5}\)

đáp số là số thập phân vô hạn không tuần hoàn