\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}\)
\(=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\)
\(=1-\frac{1}{9}\)
\(=\frac{8}{9}\)
2 / 3 + 2 / 15 + 2 / 35 + 2 / 63 + 2 / 99
= 2/1x3 + 2/3x5 + 2/5x7 + 2/7x9 + 2/9x11
= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7- 1/9 + 1/9 - 1/11 (công thức)
= 1 + 1/3 - 1/3 + 1/5 - 1/5 + 1/7 - 1/7 + 1/9 - 1/9 - 1/11 (giao hoán)
= 1 + (1/3 - 1/3) + (1/5 - 1/5) + (1/7 - 1/7) + (1/9 - 1/9) - 1/11
= 1 + 0 + 0 + 0 + 0 - 1/11 = 1 - 1/11 = 10/11
