3^{n + 2} - 2^{n + 2} + 3ⁿ - 2ⁿ = (3^{n + 2} + 3ⁿ) - (2^{n + 2} + 2ⁿ) = [3ⁿ.(3² + 1)] - [2ⁿ.(2² + 1)] = 3ⁿ.10 - 2ⁿ.5 = 3ⁿ.10 - 2^{n - 1}.10

Do: 3ⁿ.10 chia hết cho 10 và 2^{n - 1}.10 chia hết cho 10  => 3ⁿ . 10 - 2^{n - 1} . 10 chia hết cho 10  <=> 3^{n + 2} - 2^{n + 2} + 3ⁿ - 2ⁿ chia hết cho 10

(Bạn ghi sai đề chỗ 5^{n + 2} phải là 3^{n + 2} nên mình sửa lại đề và làm luôn rồi đó)

hãy xác định các tập hợp sau bằng cách chỉ ra tính chất đặc trưng của các phần tử thuộc tập hợp đó:

a) A={1;3;5;7;........;49}

b) B={11;22;33;44;........;99}

c) C={ tháng 1; tháng 3; tháng 5; tháng 7; tháng 8; tháng 10; tháng 12}

Ta có: a² + b² + c² = ab + bc + ca

=> 2(a² + b² + c²) = 2(ab + bc + ca)

=> 2a² + 2b² + 2c² = 2ab + 2bc + 2ca

=> a² + a² + b² + b² + c² + c² - 2ab - 2bc - 2ca = 0

=> (a² - 2ab + b²) + (b² - 2bc + c²) + (c² - 2ca + a²) = 0

=> (a - b)² + (b - c)² + (c - a)² = 0

<=>(a - b)² = 0 ; (b - c)² = 0 ; (c - a)² = 0

=> a = b = c

A = { 18;20; 22}         B =      {  27 ; 29  ; 31}

Exercise 8: Choose the best answer for each sentence below.

1. She doesn’t want you _________ to her arrival.
A. mention B. to mention C. mentioning D. mentions

2. Did you manage _________ _________ these parcels alone?
A. finishing / to pack B. finishing / packing C. to finish / to pack D. to finish / packing

3. Have you ever watched people _________ _________ fish?
A. try / catch B. to try / to catch C. trying / to catch D. tried / catch

4. Can someone _________ me how _________ into film from the camera’s pictures?
A. show / change B. to show / to change C. showing / change D. show / to change

5. I’ll try _________ such a foolish thing again.
A. not to cause B. to not cause C. not causing D. to cause not

6. Susan has decided _________ her friends pleased.
A. to do B. to make C. make C. do

7. Everybody would like _________ to a higher position.
A. promote B. promotes C. promoting D. to promote

8. He climbed over the wall without _________ by anybody.
A. seeing B. to see C. being seen D. to be seen

9. I remember _________ a toy car on my fifth birthday.
A. to be given B. being given C. to give D. giving

10. They always try _________ _________ the bridge as they promised before.
A. to postpone / to build B. postpone / build C. to postpone / building D. postponing / built

11. I can’t help _________ for her acceptance.
A. to wait B. waiting C. wait D. waited

12. Don’t be afraid of _________ that animal.
A. touch B. touches C. touching D. to touch

13. I am accustomed to _________ on my own.
A. living B. to live C. live D. lives
14. They are looking forward to _________ your news.
A. hear B. to hear C. hearing D. heard

15. American women have got used to _________ independently recently.
A. live B. to live C. living D. lives

16. We won’t let you_________ what we are going to do with him.
A. know B. to know C. knowing D. known

17. The manager told me _________ harder.
A. work B. working C. to work D. worked

18. Americans often say “Thank you” when you help them _________ something.
A. do B. makes C. to doing D. doing

19. I can’t help _________ anxious about the exam results.
A. to feel B. feel C. feeling D. felt

20. I can hear a cat _________ on the roof.
A. scratching B. scratches C. to scratch D. was scratching

\(E=\left\{x\in n\left|9< X< 19\right|\right\}\)

\(E=\left\{10,11,12,13,14,15,16,17,18\right\}\)

Từ 1 đến 9 cần dùng:  [(9 - 1) : 1 + 1] x 1 = 9 (chữ số)

Từ 10 đến 99 cần dùng: [(99 - 10) : 1 + 1] x 2 = 180 (chữ số)

Từ 100 đến 343 cần dùng: [(343 - 100) : 1 + 1] x 3 = 732 (chữ số)

Vậy người ta đã sử dụng tất cả: 9 + 180 + 732 = 921 (chữ số)