Question

Tính nhanh: A = \(\dfrac{5}{2.2.4}\)+\(\dfrac{5}{2.4.6}\)+\(\dfrac{5}{2.6.8}\)....+\(\dfrac{5}{2.48.50}\)

Answer 1

Em nên thêm hai phân số nữa ở sau đi nha

Answer 2

\(A=\dfrac{5}{2\cdot2\cdot4}+\dfrac{5}{2\cdot4\cdot6}+\dfrac{5}{2\cdot6\cdot8}+...+\dfrac{5}{2\cdot48\cdot50}\)

\(A=\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{2\cdot8}+...+\dfrac{5}{2\cdot48\cdot50}\)

\(A=\dfrac{5}{2+6+2\cdot8+...+2\cdot48\cdot50}\)

\(A=\dfrac{5}{2+6+8+...+48+50}\)

\(A=\dfrac{5}{\left(50-2\right)\div2+1}\)

\(A=\dfrac{5}{25}\)

Vậy \(A=\dfrac{1}{5}\)