Question

Tính giá trị biểu thức , viết kết quả dưới dạng phân số

B= \(\frac{1}{3.5.7}\) +\(\frac{1}{5.7.9}\) +\(\frac{1}{7.9.11}\) +...+\(\frac{1}{2009.2011.2013}\)

Answer 1

B=\(\frac{1}{3\cdot5\cdot7}+\frac{1}{5\cdot7\cdot9}+........+\frac{1}{2009+2011+2013}\)

\(\Leftrightarrow4B=\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+.....+\frac{4}{2009+2011+2013}\)

4B=\(\frac{1}{3\cdot5}-\frac{1}{5\cdot7}+\frac{1}{5\cdot7}-\frac{1}{7\cdot9}+......-\frac{1}{2009\cdot2011}+\frac{1}{2009\cdot2011}-\frac{1}{2011\cdot2013}\)

4B=\(\frac{1}{3\cdot5}-\frac{1}{2011\cdot2013}\)=>B=\(\left(\frac{1}{3\cdot5}-\frac{1}{2011\cdot2013}\right)\div4\)