B=1/3x5 + 1/5x7 + 1/7x9 + 1/9x11 + 1/11x13
B=1/2(2/3x5 + 2/5x7 + 2/7x9 + 2/9x11 + 2/11x13)
B=1/2(1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13)
B=1/2(1/3 - 1/13)
B=1/2 x 10/39
B=5/39
B = 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 + 1/11.13
2B = 2 ( 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 + 1/11.13 )
2B = 1/3-1/5+1/5-1/7+1/7-1/9+.....+1/11-1/13
2B = 1/3 - 1/13
2B = 10/39
B = 10/39 . 1/2
B = 10/78
\(B=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}=\frac{2}{2}\left(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{11\cdot13}\right)\)
\(=\frac{1}{2}\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{11\cdot13}\right)=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}\left[\left(\frac{1}{3}-\frac{1}{13}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+...+\left(\frac{1}{11}-\frac{1}{11}\right)\right]=\frac{1}{2}\left[\left(\frac{13}{39}-\frac{3}{39}\right)+0+...+0\right]=\frac{1}{2}\cdot\frac{10}{39}\)\(=\frac{1\cdot10}{2\cdot39}=\frac{1\cdot5}{1\cdot39}=\frac{5}{39}\)
Chúc bạn học tốt!^_^
