Question

Tính: A = \(\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\)

Answer 1

\(A=\dfrac{1}{3.5} +\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\)

\(\Rightarrow2A=2\left(\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\right)\)

\(\Rightarrow2A=\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\)

\(\Rightarrow2A=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\)

\(\Rightarrow2A=\dfrac{1}{3}-\dfrac{1}{99}=\dfrac{32}{99}\)

\(\Rightarrow A=\dfrac{32}{99}:2=\dfrac{16}{99}\)