ta có : 2b= 2/5.7+2/7.9+.....+2/99.101
2b=1/5-1/7+1/7-1/9+...+1/99-1/101
2b= (1/5-1/101)+(1/7-1/7)+(1/9-1/9)+.....(1/99-1/99)
2b= 1/5-1/101
2b= 96/505
2b= 48/505
\(\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{99.101}\)
\(=\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{101}\right)\)
\(=\frac{1}{2}.\frac{96}{505}\)
\(=\frac{48}{505}\)
_Chúc bạn học tốt_
