Có xy + x + y = 2\(\Rightarrow\) x ( y + 1 ) + ( y + 1 ) = 3 ( 2 vế cùng cộng 1 )

\(\Rightarrow\) ( x + 1 ) ( y + 1 )  = 3

\(\Rightarrow\) x + 1 và y + 1 thuộc ước của 3

Từ đó tìm ước của 3 và lập bảng để tìm x, y.

xét 2 trường hợp của n: n = 2k (số chẵn) và n = 2k + 1 (số lẻ) với k là số tự nhiên.

TH1: n(n+1) = 2k(2k +1) chia hết cho 2 (vì 2 chia hết cho 2)

TH2: n(n+1) = (2k+1)(2k+1+1)= (2k+1)(2k+2)=(2k+1)2(k+1) chia hết cho 2 (vì 2 chia hết cho 2)

Ta có điều phải chứng minh.

Ta thấy : n(n+1) là tích của 2 số tự nhiên liên tiếp

Do trong 2 số tự nhiên liên tiếp luôn có 1 số chắn => tích 2 số tự nhiên liên tiếp luôn chẵn

=>n(n+1) chẵn +> n(n+1) chia hết cho 2

Có n và n+ 1 là 2 số tự nhiên liên tiếp.

\(\Rightarrow\) n ( n + 1 ) \(⋮\) 2 ( vì trong 2 số tự nhiên liên tiếp luôn có 1 số chẵn )

Vậy n( n + 1 ) chia hết cho 2.

Tom is the most generous person I've ever met.

 Học tốt nha !!!!

Tom is the most generous people i am ever met and i am never met anyone more generous than him

1. There is a awardrobe next to my bed.

2. There is not a sofa and middle in the living room.

3. There is a cat behind the computer.

4. There are five posters under the table.

5. There is not a mirror on the wall.

6. There is a radio between a vase and a lamp.

                          Study well ! 

1, There is a wardrobe next to my bed.

2.There isn't a sofa in the middle of the living room

3,There is a cat behind the computer.

4, There are five posters underthe table

5,There isn't a mirror on the wall.

6, There is a radio between a vase and a lamp

                              Chúc bn học tốt !!!!!

Rewrite the sentences using the word given:

There/ wardrobe / next to / my bed

=>There is a wardrobe next to my bed

There/ not / sofa / middle / livingroom

=>There is not a sofa in the middle osf the livingroom

there/ cat / behind / computer

=>there is a cat behind the computer

there/ five poster/ under / table

=>there are five posters under the table

there/ not / mirror / on / wall

=>there is not a mirror  on the wall

there/ radio / beween / vase / lamp

=>there is a radio beween a vase and a lamp

a) A = 1 + 3 + 3^2 + ...+ 3^100

=> 3A = 3 + 3^2 + 3^3 + ...+ 3^101

=> 3A - A = 3¹⁰¹ - 1

2A = 3^101-1

\(A=\frac{3^{101}-1}{2}\)

b) ta co: 2A = 3¹⁰¹ - 1 ( phan a)

=> 2A + 1 = 3¹⁰¹ = 3^2.50+1

=> n = 50

a. A = 1 + 3 + 3\(^2\) + ..... + 3 \(^{100}\) 

\(\Rightarrow\) 3A  = 3 + 3\(^2\) + ... + 3 \(^{100}\) + 3 \(^{101}\) 

\(\Rightarrow\) 3 A - A = 3\(^{101}\) - 1

\(\Rightarrow\) 2A = 3\(^{101}\) - 1

\(\Rightarrow\) A = \(\frac{3^{101}-1}{2}\) 

1, That is Mr.Trung's motorbike.

2,I'm going to visit Mui Ne this summer.

3, It 's too cold so we can't go out.

4, I warm weather beacause it's good for my health.

5, My aunt is going to give her baby a birth in Setemper.

6, We are going to play volleyball this summer.

7, How old is Peterr?

          Học tốt nha !!!!

1. That is Mr. Trung's motorbike

2. I'm going to visit Mui Ne this summer

3. It's too cold so we can't go out

4. I warm weather because it's good for my health

5. My aunt is going to give her baby a birth in September

6. We are going to phay volleyball this summer

7. How old is Peter ?

                                      Wish you good study & 

                           Wish good things will come to you.

Answer:

1. There is a wardrobe next to my bed.

2. There isn't a sofa in the middle of the livingroom.

3. There is a cat behind the computer.

4. There are five poster under the table.

5. There isn't a mirror on the wall.

6. There is a radio between a vase and a lamp.

4. There are five posters under the table.
6, There is a radio between the vase and the lamp.
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