Question

tính tổng sau :

1/1.2.3 + 1/2.3.4 + ...... + 1/48.49.50

Answer 1

Đặt \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{48.49.50}\Rightarrow2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{48.49.50}=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{48.49}-\frac{1}{49.50}=\frac{1}{1.2}-\frac{1}{49.50}\)\(=\frac{1}{2}-\frac{1}{2450}=\frac{612}{1225}\Rightarrow A=\frac{306}{1225}\)