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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.
\(\Leftrightarrow x\cdot\dfrac{3}{2}-\dfrac{780}{11}:\left[\dfrac{13}{15}+\dfrac{13}{35}+\dfrac{13}{63}+\dfrac{13}{99}\right]=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}-\dfrac{780}{11}:\left[\dfrac{13}{2}\left(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}\right)\right]=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}-\dfrac{780}{11}:\left[\dfrac{13}{2}\left(\dfrac{1}{3}-\dfrac{1}{11}\right)\right]=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}-\dfrac{780}{11}:\dfrac{52}{33}=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}=40\)
hay x=40:3/2=80/3
\(\Leftrightarrow\dfrac{2}{3x}-\dfrac{780}{11}:\left[13\left(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}\right)\right]=-5\)
\(\Leftrightarrow\dfrac{2}{3x}-\dfrac{780}{11}:\left[\dfrac{13}{2}\left(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}\right)\right]=-5\)
\(\Leftrightarrow\dfrac{2}{3x}-\dfrac{780}{11}:\left[\dfrac{13}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)\right]=-5\)
\(\Leftrightarrow\dfrac{2}{3x}-\dfrac{780}{11}:\left[\dfrac{13}{2}\cdot\dfrac{8}{33}\right]=-5\)
\(\Leftrightarrow\dfrac{2}{3x}-45=-5\)
=>2/3x=40
=>3x=1/20
hay x=1/60
\(\frac{3}{2}.x-70\frac{10}{11}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}=-5\right)\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\right)=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\right]=-5\)
\(\frac{3}{2}.x-70\frac{10}{11}:\left[13\times\left(\frac{1}{3}-\frac{1}{11}\right)\right]=-5\)
\(\frac{3}{2}.x-\frac{45}{2}=-5\)
\(\frac{3}{2}.x=\frac{35}{2}\)
\(x=\frac{35}{3}\)
bài phát sai òi hihi cần mk chỉ chỗ sai ko