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\(\frac{1}{5}+\frac{1}{20}+\frac{1}{44}+\frac{1}{77}+\frac{1}{119}+\frac{1}{170}+\frac{1}{230}+\frac{1}{299}\)
\(=\frac{1}{1.5}+\frac{1}{5.4}+\frac{1}{4.11}+\frac{1}{11.7}+...+\frac{1}{23.13}\)
\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{4}+...+\frac{1}{23}-\frac{1}{13}\)
\(=1-\frac{1}{13}\)
\(=\frac{12}{13}\)
Đặt: \(\frac{1}{117}=a,\frac{1}{119}=b\)
Khi đó: \(A=3ab-4a.5.118b-5ab+\frac{8}{39}\)
\(=-2362ab+\frac{8}{39}\)
\(=-2362.\frac{1}{117}.\frac{1}{119}=\frac{38}{1071}\)
\(\frac{1}{20}+\frac{1}{44}+\frac{1}{77}+...+\frac{2}{x\left(x+3\right)}=\frac{101}{770}\)
\(\Rightarrow\)\(\frac{3}{2}.\left(\frac{1}{20}+\frac{1}{44}+\frac{1}{77}+...+\frac{2}{x\left(x+3\right)}\right)=\frac{101}{770}\).
\(\Rightarrow\)\(\frac{3}{40}+\frac{3}{88}+\frac{3}{154}+...+\frac{3}{x\left(x-3\right)}=\frac{303}{1540}\)
\(\Rightarrow\)\(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{x\left(x+3\right)}=\frac{303}{1540}\)
\(\Rightarrow\)\(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{x-1}\)
\(\Rightarrow\)\(\frac{1}{5}-\frac{1}{x+3}=\frac{303}{1540}\)
\(\Rightarrow\)\(\frac{1}{x+3}=\frac{1}{5}-\frac{303}{1540}\)
\(\Rightarrow\)\(\frac{1}{x+3}=\frac{308}{1540}-\frac{303}{1540}\)
\(\Rightarrow\)\(\frac{1}{x+3}=\frac{5}{1540}\)
\(\Rightarrow\)\(\frac{1}{x+3}=\)\(\frac{1}{308}\)
\(\Rightarrow\)\(x+3=308\)
\(\Rightarrow\)\(x=308-3\)
\(\Rightarrow\)\(x=305\)
\(\dfrac{1}{5}+\dfrac{1}{20}+\dfrac{1}{44}+\dfrac{1}{77}+\dfrac{1}{119}+\dfrac{1}{170}+\dfrac{1}{230}+\dfrac{1}{299}\)
=\(\dfrac{2}{10}+\dfrac{2}{40}+\dfrac{2}{88}+\dfrac{2}{154}+\dfrac{2}{238}+\dfrac{2}{340}+\dfrac{2}{460}+\dfrac{2}{598}\)
=\(\dfrac{1}{3}.2\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17}+\dfrac{3}{17.20}+\dfrac{3}{20.23}+\dfrac{3}{23.26}\right)\)
=\(\dfrac{2}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{26}\right)\)
=\(\dfrac{2}{3}\left(\dfrac{1}{2}-\dfrac{1}{26}\right)\)
=\(\dfrac{2}{3}.\dfrac{6}{13}\)
=\(\dfrac{4}{13}\)
4/13
k cho mk nha mk tra loi dau tien
= 4/13 nhé