Question

3/1×2 + 3/3×5 + 3/5×7 + 3/7×9 +....+3/2015×2017+3/2017×2019

Answer 1

Phân số đầu bn chép sai nhé, fai là 3/1x3 ms đúng

\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{2017.2019}\)

\(=\frac{3}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\right)\)

\(=\frac{3}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(=\frac{3}{2}.\left(1-\frac{1}{2019}\right)\)

\(=\frac{3}{2}.\frac{2018}{2019}=\frac{1009}{673}\)

Dấu . là nhân