Ta có: \(A=\frac{5}{18x23}+\frac{1}{23x24}+\frac{7}{24x31}+\frac{2}{31x33}+\frac{4}{33x37}+\frac{1}{37x38}+\frac{7}{38x45}+\frac{9}{45x54}\)
\(\Rightarrow A=\frac{1}{18}-\frac{1}{23}+\frac{1}{23}-\frac{1}{24}+\frac{1}{24}-\frac{1}{31}+...+\frac{1}{38}-\frac{1}{45}+\frac{1}{45}-\frac{1}{54}\)
\(\Rightarrow A=\frac{1}{18}-\frac{1}{54}\)
\(\Rightarrow A=\frac{3}{54}-\frac{1}{54}=\frac{1}{27}\)
Vậy \(A=\frac{1}{27}\)
*Công thức: \(\frac{a}{b.c}=\frac{1}{b}-\frac{1}{c}\left(a+b=c\right)\)
Tớ mới chuẩn bị lớp 6 thôi, ko hiểu đâu.