Question

Tìm x biết : (1/1.2.3+1/2.3.4+................+1/8.9.10).x=23/45

Answer 1

Đặt A bằng biểu thức trong ngoặc

\(2A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{10-8}{8.9.10}\)

\(2A=\dfrac{1}{2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{8.9}-\dfrac{1}{9.10}=\dfrac{1}{2}-\dfrac{1}{9.10}=\dfrac{44}{90}\)

\(A=\dfrac{22}{90}\)

\(x=\dfrac{23}{45}:A=\dfrac{23}{45}:\dfrac{22}{90}=\dfrac{23}{11}=2\dfrac{1}{11}\)