Question

[Askaban Trần]

Tìm tỉ số \(\frac{A}{B}\)biết

a,\(A=\frac{4}{7.31}+\frac{6}{7.41}+\frac{9}{10.41}+\frac{7}{10.57}\)

\(B=\frac{7}{19.31}+\frac{5}{19.43}+\frac{3}{23.43}+\frac{11}{23.57}\)

b,\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}\)

\(B=\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}\)

GIẢI RÕ NHA ! NHANH NHANH MÌNH CẦN GẤP !+_+

Answer 1

[Anh Mai]

a) Ta có: A= \(\frac{4}{7.31}+\frac{6}{7.41}+\frac{9}{10.41}+\frac{7}{10.57}\)

\(\Rightarrow\)\(\frac{1}{5}A=\frac{4}{31.35}+\frac{6}{35.41}+\frac{9}{41.50}+\frac{7}{50.57}\)

\(\Rightarrow\frac{1}{5}A=\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{41}+\frac{1}{41}-\frac{1}{50}+\frac{1}{50}-\frac{1}{57}\)

\(\Rightarrow\frac{1}{5}A=\frac{1}{31}-\frac{1}{57}\)

Ta có: \(B=\frac{7}{19.31}+\frac{5}{19.43}+\frac{3}{23.43}+\frac{11}{23.57}\)

\(\Rightarrow\frac{1}{2}B=\frac{7}{31.38}+\frac{5}{38.43}+\frac{3}{43.46}+\frac{11}{46.57}\)

\(\Rightarrow\frac{1}{2}B=\frac{1}{31}-\frac{1}{38}+\frac{1}{38}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}+\frac{1}{46}-\frac{1}{57}\)

\(\frac{1}{2}B=\frac{1}{31}-\frac{1}{57}\)

Do đó: \(\frac{1}{2}B=\frac{1}{5}A\Rightarrow\frac{A}{B}=\frac{5}{2}\)

b) Ta có: \(B=\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}\)

\(\Rightarrow B=\left(1+\frac{2015}{2}\right)+\left(1+\frac{2014}{3}\right)+...+\left(1+\frac{1}{2016}\right)+1\)

\(\Rightarrow B=\frac{2017}{2}+\frac{2017}{3}+...+\frac{2017}{2016}+\frac{2017}{2017}=2017\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}\right)\)

\(\Rightarrow\frac{A}{B}=\frac{1}{2017}\)