Question

 Tính     \(A=\frac{6}{1.4.7}+\frac{6}{4.7.10}+\frac{6}{7.10.13}+......+\frac{6}{16.19.22}\)

Answer 1

Ta có \(A=\frac{1}{1.4}-\frac{1}{4.7}+\frac{1}{4.7}-\frac{1}{7.10}+\frac{1}{7.10}-...+\frac{1}{16.19}-\frac{1}{19.22}\)

\(=\frac{1}{4}-\frac{1}{418}=\frac{207}{836}\)

Answer 2

\(A=\frac{6}{1\cdot4\cdot7}+\frac{6}{4\cdot7\cdot10}+\frac{6}{7\cdot10\cdot13}+...+\frac{6}{16\cdot19\cdot22}\)

\(A=\frac{1}{1\cdot4}-\frac{1}{4\cdot7}+\frac{1}{4\cdot7}-\frac{1}{7\cdot10}+...+\frac{1}{16\cdot19}-\frac{1}{19\cdot22}\)

\(A=\frac{1}{4}-\frac{1}{19\cdot22}=\frac{207}{836}\)