Question

Tính nhanh : 1/1*5+1/5*9+1/9*13+...+1/2013*2017

Answer 1

\(\frac{1}{1\times5}+\frac{1}{5\times9}+\frac{1}{9\times13}+...+\frac{1}{2013\times2017}\)

\(=4\times\left(\frac{1}{1\times5}+\frac{1}{5\times9}+\frac{1}{9\times13}+...+\frac{1}{2013\times2017}\right)\)

\(=4\times\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{2013}-\frac{1}{2017}\right)\)

\(=4\times\left(1-\frac{1}{2017}\right)\)

\(=4\times\frac{2016}{2017}\)

\(=\frac{8064}{2017}\)