\(A=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{99.101}\)
\(\Leftrightarrow A=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(\Leftrightarrow A=\frac{3}{2}\left(1-\frac{1}{101}\right)\)
\(\Leftrightarrow A=\frac{3}{2}.\frac{100}{101}\)
\(\Leftrightarrow A=\frac{150}{101}\)
A=3/1x3+3/3x5+3/5x7+.....+3/99x101
A=3x(1/1x3+1/3x5+1/5x7+.....+1/99x101)
A=3/2x(2/1x3+2/3x5+2/5x7+.....+2/99x101)
A=3/2x(1/1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
A=3/2x(1/1-1/101)
A=3/2x(101/101-1/101)
A=3/2x100/101
A=150/101.
Vậy A=150/101
