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M = 3/4 - 3/5 + 3/7 + 3/11 / 13/4 - 13/5 + 13/7 + 13/11
M = 3.(1/4 - 1/5 + 1/7 + 1/11) / 13.(1/4 - 1/5 + 1/7 + 1/11)
M = 3/13
M = 3/4 - 3/5 + 3/7 + 3/11 / 13/4 - 13/5 + 13/7 + 13/11
M = 3.(1/4 - 1/5 + 1/7 + 1/11) / 13.(1/4 - 1/5 + 1/7 + 1/11)
M = 3/13
Ta có \(M=\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}=\frac{3\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}=\frac{3}{4}\)
ta có
đặt 3/5+3/7-3/11=N=> N=3*(1/5+1/7-1/11)
đặt 4/5+4/7-4/11=P=> P=4*(1/5+1/7-1/11)
=> N/P=3*(1/5+1/7-1/11)/4*(1/5+1/7-1/11)=> M=3/4
\(M=\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}=\frac{3\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}=\frac{3}{4}\)
- Ta co \(M=\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}\)\(=\frac{3\times\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{4\times\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}\)\(=\frac{3}{4}\)
2. Goi d la uoc chung lon nhat cua n va n+1 thi \(n⋮d\) va \(n+1⋮d\)
\(\Rightarrow n+1-n⋮d\Rightarrow1⋮d\Rightarrow d\in\left[1;-1\right]\)
Vay \(\frac{n}{n+1}\)la phan so toi gian
\(\Rightarrow A=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{95.99}\)
\(A=4\left(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{95.99}\right)\)
\(A=4.\frac{1}{4}\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{99}\right)\)
\(A=\frac{4}{4}\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(A=\frac{32}{99}\)
\(\frac{4}{3}.\frac{4}{7}+\frac{4}{7}.\frac{4}{11}+\frac{4}{11}.\frac{4}{15}+...+\frac{4}{95}.\frac{4}{99}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{99}\)
\(=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)
\(\Leftrightarrow A=\frac{32}{99}\)
\(\frac{\frac{3}{5}+\frac{3}{7}+\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}+\frac{4}{11}}\)=3.\(\frac{3\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}\)=\(\frac{3}{4}\)
\(M=\frac{3.\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{11}\right)}{4.\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{11}\right)}=\frac{3}{4}\)