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Đặt tích 3 số tự nhiên liên tiếp là A = a.(a+1)(a+2)
Để chứng minh A chia hết cho 2 có 2 trường hợp :
+) Nếu a chia hết cho 2 ( a chẵn ) => A chia hết cho 2
+) Nếu A chia 2 dư 1 ( a lẻ ) => a+1 chia hết cho 2 => A chia hết cho 2
Để chứng minh A chia hết cho 3 có 3 trường hợp :
+) Nếu A chia hết cho 3 => A chia hết cho 3
+) Nếu A chia 3 dư 1 => a+2 chia hết cho 3 => A chia hết cho 3
+) Nếu A chia 3 dư 2 => a+1 chia hết cho 3 => A chia hết cho 3
Mà 2 và 3 là 2 số nguyên tố cùng nhau nên :
A chia hết cho 6 hay 3 số tự nhiên liên tiếp chia hết cho 6
Số học sinh lớp 6A là:
\(120.\dfrac{1}{3}=40\left(hs\right)\)
Số học sinh lớp 6B là:
\(120.\dfrac{3}{8}=45\left(hs\right)\)
Số học sinh lớp 6C là:
\(120-40-45=35\left(hs\right)\)
Dịch ra là: Ta có: 3A = 3. (1 + 3 + 32 + 33 + ... + 399 + 3100) (1 + 3 + 32 + 33 + ... + 399 + 3100) 3A = 3 + 32 + 33 + ... + 3100 + 31013 + 32 + 33 + ... + 3100 + 3101 Suy ra: 3A - A = (3 + 32 + 33 + ... + 3100 + 3101) - (1 + 3 + 32 + 33 + ... + 399 + 3100) (3 + 32 + 33 + ... + 3100 + 3101) - (1 + 3 + 32 + 33 + ... + 399 + 3100) ⇒⇒ A = 3101−123101−12 Vậy A = 3101−12
Mà đoạn 2A sai nhé bạn, sửa lại:
2A = 3101−13101−1 2A=-10001
A=-10001/2
A=-5000,5
Vậy A=-5000,5
2. Tìm lỗi sai ở những câu sau và sửa lại cho đúng.
1. She am tall. -> is
2. I are Minh. -> am
3. We am fine, thank you. -> are
4. They is cats. -> are
5. Peter are a student. -> is
6. We is students. -> are
7. They is my friends. -> are
8. Here are my book. -> is
9. Tom are my friend. -> is
3. Fill in the blank with suitable form of present verb of TO BE:
1. Today ......is...... Monday. I .........am..... at school.
2. Mom and Dad ………are………..at home. They ........are...... at the hospital.
3. The weather……is………… nice. It ....is............. windy and rainy.
4. …Is…… he free all day?
5. She……is……….tired.
6. I……am……… in London.
7. ……Are…you at Nina’s house?
8. I……am……with him.
9. ……Are……..they happy?
10. He……is…… at school. He is at home.
11. .....Are...... you busy today? - Yes, I……am………
12. ……Is…. it cold? - No, it……isn't……….
13. Where……are……… they on Sunday? - They……are……. at the store.
14. ……Are……Nina and Sam strong? - No, they…aren't……………
15. ……Is…….Sam ill? - Yes, she………is…………
4. Fill in the blank with suitable form of past verb of TO BE:
1. Yesterday ....was.... Monday. I ....was... at school.
2. Mom and Dad ……were…………..at home yesterday. They were at the hospital.
3. The weather………is……… nice. It was windy and rainy.
4. …Was…… he free all day yesterday?
5. She……was……….tired last night.
6. I……was……… in London last month.
7. …Were……you at Nina’s house yesterday?
8. I……was……with him yesterday.
9. ……Were……..they happy last week?
10. He……was…… at school. He was at home.
11. Were you busy yesterday? - Yes, I…was…………
12. ……Was…. it cold last night? - No, it……wasn't………. It was hot.
13. Where……were……… they on Saturday? - They…were………. at the store.
14. ……Were……Nine and Bill strong this morning? - No, they…weren't…15. ……Was…….Jimmy ill last night? - Yes, he ……was……………
5. Fill the blank with am/ is/ are.
1.The film __is___interesting.
2. His father __is_____a dentist.
3. Children ___are___ in the classroom.
4. Your dog __is____ nice.
5. I __am___busy.
6. She __is____my best friend.
7. We ___are____here.
8. John __is____at home.
9. They ___are___ good people.
10.My parents ___are____teachers.
6. Complete the sentence with AM/ IS/ ARE
1. It …………is…………… rainy and cool today.
2. I …………am…………… at my office now.
3. They …………are…………… from Australia.
4. There ………is……………… a laptop on the desk.
5. My name ……is………………… Nga.
6. We …………are…………… Russian.
7. That ………is……………… not true.
8. I …………am…………… not too bad, thanks.
9. Giang and Nguyet ……are………………… married.
10. She ………is……………… a Math teacher.
11. This computer ……is………………… him.
12. Jane and Peter ……are………………… single.
13. My brother …………is…………… at the school now.
14. Many people ………are……………… in the shopping mall.
15. We …………are…………… in Viet Nam.
16. It …………is…………… Saturday today.
17. I ……………an………… an content editor.
18. My name ………is……………… Thu.
19. There …………are…………… many people in this classroom.
20. ……Is……… Annie your sister?
7. Complete the sentences with am, is or are.
1. A: Where's Jack?
B: He __is____ playing football with his classmates.
2. A: Let's play table tennis!
B: Sorry. We __are____ having dinner at the moment.
3. A: Where are Linda and Kate?
B: They __are____ shopping. They want to buy dresses for their summer holiday.
4. A: Are you OK?
B: Yes, I __am_ having great fun. What about you?
5. A: Please help me.
B: Sorry. I __am_ reading a book about panda.
6. A: Can I talk to Lan, please?
B: She isn't at home. She ____is___ riding her bike with her brother.
b.(a+b)-(b-a)+c=2a+c
Xét VT: (a+b)-(b-a)+c = a + b - b + a + c = 2a+c
Mà VP = 2a+c
=> VT = VP
c.-(a+b-c)+(a-b-c)=-2b
Xét VT: -(a+b-c)+(a-b-c) = -a - b + c + a - b - c = -2b
Mà VP = -2b
=> VT = VP
d.a(b+c)-a(b+d)=a(c-d)
Xét VT: a(b+c)-a(b+d) = ab + ac - ab - ad = ac - ad = a(c-d)
Mà VP = a(c-d)
=> VT = VP
e.a(b-c)+a(d+c)=a(b+d)
Xét VT: a(b-c)+a(d+c)= ab -ac + ad + ac = ab + ad = a(b+d)
Mà VP = a(b+d)
=> VT = VP
Tiếng Anh.
1. My father works for a company (1)……from……… Monday (2) ……to……… Friday.
2. He lives (3)………in…………………. a house (4) ………in……… the countryside.
3. Lan is standing near the store and she is waiting (5) ………for…………… the bus.
4. I agree (6)……with…..… you about that.
5. I the weather (7) ……in…… June.
6. Look (8) ………at…………… the picture (9) ………on……….. the wall, please.
7. The desk is (10)……between……………. the chair and the bed.
1.
3A= 3(3+32+ ...+ 32017)
3A= 32 + 33 + .... + 32018
Lấy 3A - A = (32 + 33 +...+ 32018) - (3+32+...+32017)
2A = 32018 - 3
2A+3 = 32018 - 3 +3 = 32018
=> 2A+3 là một lũy thừa của 3