Question

3/5x7+3/7x9+......+3/129x131 

Giai nhanh giúp mik nha các bn 

Answer 1

\(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+...+\frac{3}{129\cdot131}\)

\(=3\left(\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+....+\frac{1}{129\cdot131}\right)\)

\(=\frac{3}{2}\left(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{129\cdot131}\right)\)

\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{129}-\frac{1}{131}\right)\)

\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{131}\right)\)

\(=\frac{3}{2}\cdot\frac{126}{655}\)

\(=\frac{378}{1310}=\frac{189}{655}\)