Áp dụng tính chất (a - b)(a + b) = a² + ab - ab - b² = a² - b²

Ta có : \(A=\frac{3}{\left(1.2\right)^2}+\frac{5}{\left(2.3\right)^2}+...+\frac{19}{\left(9.10\right)^2}\)

\(=\frac{1}{1.2}.\frac{3}{1.2}+\frac{1}{2.3}.\frac{5}{2.3}+...+\frac{1}{9.10}.\frac{19}{9.10}\)

\(=\left(1-\frac{1}{2}\right)\left(1+\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{1}{2}+\frac{1}{3}\right)+...+\left(\frac{1}{9}-\frac{1}{10}\right)\left(\frac{1}{9}+\frac{1}{10}\right)\)

\(=1^2-\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^2-\left(\frac{1}{3}\right)^2+...+\left(\frac{1}{9}\right)^2-\left(\frac{1}{10}\right)^2=1^2-\left(\frac{1}{10}\right)^2=1-\frac{1}{100}=\frac{99}{100}< 1\)

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Bài 1: tìm lỗi sai

1. She goes to visit her grandmother and grandfather next week

=> will go

2. Which place is Phuong and Mai going to visit firts?

=> are

3. They are going in vacation this summer

=> on

4. He wants visit the temple and take some photos

=> to visit

5. They always are going to have a picnic in the park on the weekend

=>  \(\varnothing\)

6. It is on of the higher mountains in the world

=> highest

7. This city has a population for 6.3 milion

=> of

8. She always go to Hong Kong on summer vacation

=> goes

9. The River Nile is 6,437 kilometers length

=> long

10. Tomorrow, I am going to visiting the Tower of LonDon

=> am going to visit