Question

[pluto]

Tính A/B biết :

A = 1/1.300 + 1/2.301 + 1/3.302 + ... + 1/101.400

B = 1/1.102 + 1/2.103 + 1/3.104 + ...+ 1/299.400

Answer 1

[Đức Phạm]

\(A=\frac{1}{1.300}+\frac{1}{2.301}+\frac{1}{3.302}+...+\frac{1}{101.400}\)

\(A=\frac{1}{299}.\left(\frac{1}{1}-\frac{1}{300}+\frac{1}{2}-\frac{1}{301}+\frac{1}{3}-\frac{1}{3012}+...+\frac{1}{101}-\frac{1}{400}\right)\)

\(A=\frac{1}{299}.\left(\frac{1}{1}-\frac{1}{400}\right)\)

\(A=\frac{1}{299}.\frac{399}{400}\)

\(A=\frac{399}{119600}\)

\(B=\frac{1}{1.102}+\frac{1}{2.103}+\frac{1}{3.104}+...+\frac{1}{299.400}\)

\(B=\frac{1}{101}.\left(\frac{1}{1}-\frac{1}{102}+\frac{1}{2}-\frac{1}{103}+....+\frac{1}{299}-\frac{1}{400}\right)\)

\(B=\frac{1}{101}.\left(\frac{1}{1}-\frac{1}{400}\right)\)

\(B=\frac{1}{101}.\frac{399}{400}\)

\(B=\frac{399}{40400}\)

\(\Rightarrow\frac{A}{B}=\frac{399}{\frac{119600}{\frac{399}{40400}}}=\frac{101}{299}\)