Question

Thực hiện phép tính:

J) \(\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{53.55}\)

Answer 1

Ta có: 

\(\dfrac{2}{5.7}=\dfrac{7-5}{5.7}=\dfrac{1}{5}-\dfrac{1}{7}\)

\(\dfrac{2}{7.9}=\dfrac{9-7}{7.9}=\dfrac{1}{7}-\dfrac{1}{9}\)

..........

\(\dfrac{2}{53.55}=\dfrac{55-53}{53.55}=\dfrac{1}{53}-\dfrac{1}{55}\)

\(\Rightarrow\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{53.55}=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{5}+...+\dfrac{1}{53}-\dfrac{1}{55}=\dfrac{1}{5}-\dfrac{1}{55}=\dfrac{10}{55}=\dfrac{2}{11}\)

Answer 2

\(=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{53}-\dfrac{1}{55}=\dfrac{1}{5}-\dfrac{1}{55}=\dfrac{2}{11}\)

Answer 3

2/11