Question

[Hoàng Hà Phương]

Ai giúp gấp đi ạ !

Tính nhanh 

A) B =3/2×5+3/5×8+3/8×11+3/11×14

B)3/1×2+3/2×3+3/3×4+...+3/99×100

C)4 /3×7+4/7×11+4/11×15+4/15×19+4/19×23+4/23×27

D) (1-1/3)×(1-1/4)×(1-1/5)×(1-1/6)×...×(1-1/99)

Answer 1

[Edogawa Conan]

a) \(B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}\)

      \(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}-\frac{1}{8}+\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)

       \(=\frac{1}{2}-\frac{1}{14}=\frac{3}{7}\)

b) Ta có : A = \(\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{99.100}\)

                  \(=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

                   \(=3.\left(1-\frac{1}{100}\right)\)

                     \(=3.\frac{99}{100}=\frac{297}{100}\)