Question

[Võ Đông Anh Tuấn]

12·6 +14·9 +16·12 +...+136·57 +138·60  

Answer 1

[Phạm Tuấn Kiệt]

\(\frac{1}{2.6}+\frac{1}{4.9}+\frac{1}{6.12}+...+\frac{1}{36.57}+\frac{1}{38.60}\)

\(=\frac{1}{2.3\left(1.2\right)}+\frac{1}{2.3\left(2.3\right)}+\frac{1}{2.3\left(3.4\right)}+...+\frac{1}{2.3\left(18.19\right)}+\frac{1}{2.3\left(19.20\right)}\)

\(=\frac{1}{6}.\left(\frac{6}{6\left(1.2\right)}+\frac{6}{6\left(2.3\right)}+\frac{6}{6\left(3.4\right)}+...+\frac{6}{6\left(18.19\right)}+\frac{6}{6\left(19.20\right)}\right)\)

\(=\frac{1}{6}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

\(=\frac{1}{6}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(=\frac{1}{6}\left(1-\frac{1}{20}\right)\)

\(=\frac{1}{6}.\frac{19}{20}=\frac{19}{120}\)