Question

Tính tỉ số A/B biết: A=1/22.32+1/3.3+...+1/1073.2003

B=1/2.1974+1/3.1975+...+1/31.2003

Answer 1

vào câu hỏi tương tự

Answer 2

Câu tìm câu hỏi tương tự mà nghĩ ra

Answer 3

Ta có : \(A=\frac{1}{2.32}+\frac{1}{3.33}+...+\frac{1}{1973.2003}\)

\(=\frac{1}{30}\left(\frac{1}{2}-\frac{1}{32}+\frac{1}{3}-\frac{1}{33}+....+\frac{1}{1973}-\frac{1}{2003}\right)\)

\(=\frac{1}{30}\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{31}-\frac{1}{1974}-\frac{1}{1975}-...-\frac{1}{2003}\right)\)

Lại có : \(B=\frac{1}{2.1974}+\frac{1}{3.1975}+...+\frac{1}{31.2003}\)

\(=\frac{1}{1972}\left(\frac{1}{2}-\frac{1}{1974}+\frac{1}{3}-\frac{1}{1975}+....+\frac{1}{31}-\frac{1}{2003}\right)\)

\(=\frac{1}{1972}\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{31}-\frac{1}{1974}-\frac{1}{1975}-...-\frac{1}{2003}\right)\)

Khi đó : \(\frac{A}{B}=\frac{1972}{30}\)

Answer 4

\(\frac{986}{15}\)

Answer 5

986/15