C=\(\dfrac{5}{27.29}+\dfrac{5}{29.31}+...+\dfrac{5}{73.75}\)
C=\(\dfrac{5}{2}.\left(\dfrac{2}{27.29}+\dfrac{2}{29.31}+...+\dfrac{2}{73.75}\right)\)
C=\(\dfrac{5}{2}.\left(\dfrac{2}{27}-\dfrac{2}{29}+\dfrac{2}{29}-\dfrac{2}{31}+...+\dfrac{2}{73}-\dfrac{2}{75}\right)\)
C=\(\dfrac{5}{2}.\left(\dfrac{2}{27}-\dfrac{2}{75}\right)\)
C=\(\dfrac{5}{2}.\dfrac{32}{675}=\dfrac{16}{135}\)
D làm tương tự
c) Ta có: \(C=\dfrac{5}{27\cdot29}+\dfrac{5}{29\cdot31}+...+\dfrac{5}{73\cdot75}\)
\(=\dfrac{5}{2}\left(\dfrac{2}{27\cdot29}+\dfrac{2}{29\cdot31}+...+\dfrac{2}{73\cdot75}\right)\)
\(=\dfrac{5}{2}\left(\dfrac{1}{27}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{31}+...+\dfrac{1}{73}-\dfrac{1}{75}\right)\)
\(=\dfrac{5}{2}\cdot\left(\dfrac{1}{27}-\dfrac{1}{75}\right)\)
\(=\dfrac{5}{2}\cdot\dfrac{16}{675}=\dfrac{8}{135}\)
d) Ta có: \(D=\dfrac{6}{7\cdot12}+\dfrac{6}{12\cdot17}+...+\dfrac{6}{52\cdot57}\)
\(=\dfrac{6}{5}\left(\dfrac{5}{7\cdot12}+\dfrac{5}{12\cdot17}+...+\dfrac{5}{52\cdot57}\right)\)
\(=\dfrac{6}{5}\left(\dfrac{1}{7}-\dfrac{1}{57}\right)\)
\(=\dfrac{6}{5}\cdot\dfrac{50}{399}=\dfrac{20}{133}\)
