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Rút gọn biểu thức S, ta có:
\(S=\frac{13}{30}+\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(\Leftrightarrow S=\frac{13}{30}+\left(\frac{13}{3\cdot5}+\frac{13}{5\cdot7}+\frac{13}{7\cdot9}+\frac{13}{9\cdot11}\right)\)
Đặt \(P=\frac{13}{3\cdot5}+\frac{13}{5\cdot7}+\frac{13}{7\cdot9}+\frac{13}{9\cdot11}\)
\(\Rightarrow P\cdot\frac{2}{13}=\frac{2}{3.5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\)
\(\Rightarrow P\cdot\frac{2}{13}=\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+\frac{2}{7}-\frac{2}{9}+\frac{2}{9}-\frac{2}{11}\)
\(\Rightarrow P\cdot\frac{2}{13}=\frac{2}{3}-\frac{2}{11}\)
\(\Rightarrow P\cdot\frac{2}{13}=\frac{16}{33}\)
\(\Rightarrow P=\frac{104}{33}=3\frac{5}{33}\)
Ta có: \(P+1>P+\frac{13}{30}\)
Mà \(P+\frac{13}{30}=S\)
Còn \(P+1=3\frac{5}{33}+1=4\frac{5}{33}<5\)
\(\Rightarrow S<4\frac{5}{33}<5\)
Vậy đề bài sai.
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\(\frac{3}{2}.x-70\frac{10}{11}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}=-5\right)\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\right)=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3}-\frac{1}{11}\right)\right]=-5\)
\(\frac{3}{2}.x-\frac{45}{2}=-5\)
\(\frac{3}{2}.x=\frac{35}{2}\)
\(x=\frac{35}{3}\)
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a) \(\frac{5252}{7575}=\frac{52}{75};\frac{525252}{757575}=\frac{52}{75}\)
Vậy cả 3 phân số trên bằng nhau
b) \(\frac{1313}{1515}=\frac{13}{15};\frac{131313}{151515}=\frac{13}{15}\)
Vậy các phân số trên bằng nhau
\(\frac{52}{73}=\frac{52\cdot101}{73\cdot101}=\frac{5252}{7373}\)
\(\frac{52}{73}=\frac{52\cdot10101}{73\cdot10101}=\frac{525252}{737373}\)
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\(\frac{52}{75}=\frac{52.101}{75.101}=\frac{5252}{7575};\frac{52}{75}=\frac{52.10101}{75.10101}=\frac{525252}{757575}\)
\(\frac{13}{15}=\frac{13.101}{15.101}=\frac{1313}{1515};\frac{13}{15}=\frac{13.10101}{15.10101}=\frac{131313}{151515}\)
\(\frac{ab}{cd}=\frac{101ab}{101cd}=\frac{abab}{cdcd};\frac{ab}{cd}=\frac{10101ab}{10101cd}=\frac{ababab}{cdcdcd}\)
ai k minh minh k lai
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\(A=\frac{2013.10001}{2014.10001}=\frac{2013}{2014}=1-\frac{1}{2014}\)A=(2013.10001)/(2014.10001)=2013/2014=1-1/2014
B=(13.10101)/(14.10101)=13/14=1-1/14
Ta thấy 1/14>1/2014 => 1-1/2014>1-1/14 => A>B
\(\frac{131313}{151515}=\frac{13.10101}{15.10101}=\frac{13}{15}\)
\(\frac{13026}{15030}=\frac{13.1002}{15.1002}=\frac{13}{15}\)
=> \(\frac{131313}{151515}=\frac{13026}{15030}\left(=\frac{13}{15}\right)\)