Question

3/5*7 + 3/7*9 + ...... + 3/117*119 = ? 

Viết đáp ra giúp mik nhé ( giải luôn ra cũng đc ) 

Answer 1

\(\frac{3}{5\times7}+\frac{3}{7\times9}+...+\frac{3}{117\times119}\)

\(=\frac{3}{2}\times\left(\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{117\times119}\right)\)

\(=\frac{3}{2}\times\left(\frac{7-5}{5\times7}+\frac{9-7}{7\times9}+...+\frac{119-117}{117\times119}\right)\)

\(=\frac{3}{2}\times\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{117}-\frac{1}{119}\right)\)

\(=\frac{3}{2}\times\left(\frac{1}{5}-\frac{1}{119}\right)=\frac{171}{595}\)