Question

Tính nhanh 

B=4/2*5+4/5*8+4/8*11+...+4/44*47+4/47*50

Answer 1

Ta có:

\(B=\frac{4}{2.5}+\frac{4}{5.8}+...+\frac{4}{47.50}\)

     \(=4.\left(\frac{1}{2.5}+\frac{1}{5.8}+...+\frac{1}{47.50}\right)\)

\(\Rightarrow3B=4.\left(3.\left(\frac{1}{2.5}+\frac{1}{5.8}+...+\frac{1}{47.50}\right)\right)\)

              \(=4.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{47.50}\right)\)

              \(=4.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{47}-\frac{1}{50}\right)\)

              \(=4.\left(\frac{1}{2}-\frac{1}{50}\right)\)

              \(=4.\frac{12}{25}\)

               \(=\frac{48}{25}\)

\(\Rightarrow B=\frac{48}{25}:3=\frac{16}{25}\)