Question

Tính tổng A= 1/2.4 + 1/4.6+.... +1/48.50

Answer 1

Ta có: \(A=\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+...+\frac{1}{48\cdot50}\)

\(\Rightarrow2\cdot A=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{48\cdot50}\)

\(\Rightarrow2\cdot A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{48}-\frac{1}{50}\)

\(\Rightarrow2\cdot A=\frac{1}{2}-\frac{1}{50}=\frac{12}{25}\)

\(\Rightarrow2\cdot A=\frac{12}{25}\)

hay \(A=\frac{12}{25}:2=\frac{12}{25}\cdot\frac{1}{2}=\frac{12}{50}=\frac{6}{25}\)