3/15+3/35+...+3/399
Đặt S=3/15+3/35+...+3/399
=> S=3/3.5+3/5.7+..+3/19.21
=> S=(3/3.5+3/5.7+...+3/19.21).2
=> S=2.3/3.5+2.3/5.7+...+2.3/19.21
=> S=3.(2/3.5+2/5.7+...+2/19.21)
=> S=3.(1/3-1/5+1/5-1/7+...+1/19-1/21)
=> S=3.(1/3-1/21)
=> S=3.2/7
=> S=6/7
Vậy 3/15+3/35+...+3/399=6/7
\(\frac{3}{15}+\frac{3}{35}+\frac{3}{63}+...+\frac{3}{399}\)
\(=\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{399}\)
\(=\frac{3}{2}.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(=\frac{3}{2}.\frac{2}{7}\)
\(=\frac{3}{7}\)
