Question

a) chứng tỏ 1/2.3=1/2-1/3;1/3.4=1/3-1/4 b) áp dụng câu a hãy tính tính tổng sau A= 1/5.6+1/6.7+1/7.8+...+1/2019.2020

Answer 1

a) Ta có:

      1/( 2.3 ) = ( 3 - 2 )/( 2.3 )

                     = 3/( 2.3 ) - 2/( 2.3 )

                     = 1/2 - 1/3.

     1/( 3.4 ) = ( 4 - 3 )/( 3.4 )

                     = 4/( 3.4 ) - 3/( 3.4 )

                     = 1/3 - 1/4.

b) 

Ta có:

A = 1/( 5.6 ) + 1/( 6.7 ) + 1/( 7.8 ) + ..... + 1/( 2019.2020 )

A = 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ..... + 1/2019 - 1/2020

A = 1/5 - 1/2020

A = 403/2020

Vậy A = 403/2020.

Answer 2

a) Ta có: \(\frac{1}{2.3}=\frac{3-2}{2.3}=\frac{3}{2.3}-\frac{2}{2.3}=\frac{1}{2}-\frac{1}{3}\)

\(\frac{1}{3.4}=\frac{4-3}{3.4}=\frac{4}{3.4}-\frac{3}{3.4}=\frac{1}{3}-\frac{1}{4}\)

b) Ta có: \(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+.......+\frac{1}{2019.2020}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+........+\frac{1}{2019}-\frac{1}{2020}\)

\(=\frac{1}{5}-\frac{1}{2020}=\frac{403}{2020}\)