Question

[Cao Thị Ngọc Huyền]

Tính nhanh

1/3*5 + 1/5*7 + 1/7*9 + .....+ 1/29*31 + 1/31*33

Answer 1

[Đinh Đức Hùng]

Đặt A = \(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{31.33}\)

=> 2A = \(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.....+\frac{2}{31.33}\)

=> 2A = \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{31}-\frac{1}{33}\)

=> 2A = \(\frac{1}{3}-\frac{1}{33}\)

=> A = \(\left(\frac{1}{3}-\frac{1}{33}\right):2\)