Em tham khảo
A=$\frac{4}{7×31}$+$\frac{6}{7×41}$+ $\frac{9}{10×41}$+ $\frac{7}{10×51}$
⇒$\frac{1}{5}$ A=$\frac{1}{31}$-$\frac{1}{35}$+$\frac{1}{35}$-$\frac{1}{41}$+ $\frac{1}{50}$- $\frac{1}{50}$- $\frac{1}{51}$
⇒$\frac{1}{5}$A= $\frac{1}{31}$- $\frac{1}{51}$
⇒A=$\frac{100}{1581}$
B=$\frac{7}{19×31}$+ $\frac{5}{19×43}$+..+ $\frac{11}{23×57}$
⇒$\frac{1}{2}$B= $\frac{1}{31}$- $\frac{1}{38}$+$\frac{1}{38}$+..- $\frac{1}{57}$
⇒$\frac{1}{2}$B= $\frac{1}{31}$-$\frac{1}{57}$
⇒B= $\frac{52}{1767}$
Do đó $\frac{A}{B}$= $\frac{475}{221}$
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