kb nha
1+1=?
2+2=?
3+3=?
K
Khách
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10 tháng 10 2021
\(1,\)
\(a,\) Sửa: \(A=10^n+72n-1⋮81\)
Với \(n=1\Leftrightarrow A=10+72-1=81⋮81\)
Giả sử \(n=k\Leftrightarrow A=10^k+72k-1⋮81\)
Với \(n=k+1\Leftrightarrow A=10^{k+1}+72\left(k+1\right)-1\)
\(A=10^k\cdot10+72k+72-1\\ A=10\left(10^k+72k-1\right)-648k+81\\ A=10\left(10^k+72k-1\right)-81\left(8k-1\right)\)
Ta có \(10^k+72k-1⋮81;81\left(8k-1\right)⋮81\)
Theo pp quy nạp
\(\Rightarrow A⋮81\)
\(b,B=2002^n-138n-1⋮207\)
Với \(n=1\Leftrightarrow B=2002-138-1=1863⋮207\)
Giả sử \(n=k\Leftrightarrow B=2002^k-138k-1⋮207\)
Với \(n=k+1\Leftrightarrow B=2002^{k+1}-138\left(k+1\right)-1\)
\(B=2002\cdot2002^k-138k-138-1\\ B=2002\left(2002^k-138k-1\right)+276138k+1863\\ B=2002\left(2002^k-138k-1\right)+207\left(1334k+1\right)\)
Vì \(2002^k-138k-1⋮207;207\left(1334k+1\right)⋮207\)
Nên theo pp quy nạp \(B⋮207,\forall n\)
10 tháng 10 2021
\(2,\)
\(a,\) Sửa đề: CMR: \(1\cdot2+2\cdot3+...+n\left(n+1\right)=\dfrac{n\left(n+1\right)\left(n+2\right)}{3}\)
Đặt \(S_n=1\cdot2+2\cdot3+...+n\left(n+1\right)\)
Với \(n=1\Leftrightarrow S_1=1\cdot2=\dfrac{1\cdot2\cdot3}{3}=2\)
Giả sử \(n=k\Leftrightarrow S_k=1\cdot2+2\cdot3+...+k\left(k+1\right)=\dfrac{k\left(k+1\right)\left(k+2\right)}{3}\)
Với \(n=k+1\)
Cần cm \(S_{k+1}=1\cdot2+2\cdot3+...+k\left(k+1\right)+\left(k+1\right)\left(k+2\right)=\dfrac{\left(k+1\right)\left(k+2\right)\left(k+3\right)}{3}\)
Thật vậy, ta có:
\(\Leftrightarrow S_{k+1}=S_k+\left(k+1\right)\left(k+2\right)\\ \Leftrightarrow S_{k+1}=\dfrac{k\left(k+1\right)\left(k+2\right)}{3}+\left(k+1\right)\left(k+2\right)\\ \Leftrightarrow S_{k+1}=\dfrac{\left(k+1\right)\left(k+2\right)\left(k+3\right)}{3}\)
Theo pp quy nạp ta có đpcm
\(b,\) Với \(n=0\Leftrightarrow0^3=\left[\dfrac{0\left(0+1\right)}{2}\right]^2=0\)
Giả sử \(n=k\Leftrightarrow1^3+2^3+...+k^3=\left[\dfrac{k\left(k+1\right)}{2}\right]^2\)
Với \(n=k+1\)
Cần cm \(1^3+2^3+...+k^3+\left(k+1\right)^3=\left[\dfrac{\left(k+1\right)\left(k+2\right)}{2}\right]^2\)
Thật vậy, ta có
\(1^3+2^3+...+k^3+\left(k+1\right)^3\\ =\left[\dfrac{k\left(k+1\right)}{2}\right]^2+\left(k+1\right)^3\\ =\dfrac{k^2\left(k+1\right)^2+4\left(k+1\right)^3}{4}=\dfrac{\left(k+1\right)^2\left(k^2+4k+4\right)}{4}\\ =\dfrac{\left(k+1\right)^2\left(k+2\right)^2}{4}=\left[\dfrac{\left(k+1\right)\left(k+2\right)}{2}\right]^2\)
Theo pp quy nạp ta được đpcm
LH
2
MN
2 tháng 6 2021
1. Mike can’t buy that car because he doesn’t have enough money.
Mike can’t afford to buy that car_____________.
2. Susan looks forward to see her father soon.
Susan hopes to see her father soon _______________________________________________.
3. She said she didn’t breaking the vase.
aShe denied breaking the vase._______________________________________________.
4. She is thinking about going picnic this weekend.
She is considering going picnic this weekend _______________________________________________.
5. She said she would play badminton with her friends this afternoon.
aShe decided to play badminton with her friends this afternoon. _______________________________________________.
6. She can’t put up with this short of money anymore.
aShe can’t stand this short of money anymore. _______________________________________________.
7. These windows will have to be cleaned again.
aThese windows need to be cleaned again. ____________________________________________.
8. The police told us not to go out of this building.
aThe police warned us not to go out of this building._______________________________________________.
9.She refused to steal the car.
She denied stealing the car _______________________________________________.
10. Manny said he didn’t stole the car, but he said he borrowed it.
Manny denied stealing the car._______________________________________________
H
11 tháng 3 2021
1.Nam said that he was reading a novel
2.Lan said that she always drink milk everyday
3.This boy told me that his father works in a office
4.My friend said that they would go to the theater the next day
5.Jun said that thay had drunk three cups of tea that night
6.Peter told her that he would arrive before his brother
7.My teacher told us not to forget to do that homework
DT
Đỗ Thanh Hải
CTVVIP
1 tháng 4 2021
1 I can't eat or speak because I have a sore throat
2 I usually play badminton in my free time
3 What would your brother like to be in the future?
4 Why shouldn't he climb the tree? Because it may break your arm (câu này hơi ngang)
5 Mai is playing with matches. She may start a fire
1 tháng 4 2021
1. I can't speak or eat because I have a sore throat.
2. I usually play badminton in my free time.
3.What would your brother like to be in the future?
4. Why he should't climb the tree? Because you may break your arms.
5. Mai is playing with matches. She may start a fire.
TP
18 tháng 3 2022
V/ Mistake recognition - Sửa giúp mình luôn nha
1. They haven’t already done their /homework.
=> They haven't done their homework yet
2. The little girl has stand here for hours to wait/ for the bus.
has stand => has stood
3. Last summer, we took part in many community services such as helping the elderly, cleaning streets and donate books.
donate => donating
4. When I was young child, I loved /going fishing with my father.
young child => young/a child
5. The man next door prefers staying home/ to taking part/ in community services.
to taking => to take
HN
15 tháng 1 2023
1.as well as-> and
2.are->is
3.differently(S+be+adv+adj vì shaped là adj)
4.the worst->the worse(trc là so sánh hơn thì sau cx phải so sánh hơn)
5.less->fewer(friends đếm đc)
Ai đúng thì chúc mừng:D
B
15 tháng 1 2023
1. Vaslov->Vaslav Nijinsky achieved world recognition as both a dancer as well as->and a choreographer.
2. Lack of sanitation in restaurants are->is a major cause of disease in some areas of the country.
3. This vase has the same design, but it is different->differently shaped from that one.
4. The harder he tried, the worst->worse he danced before the large audience.
5. He has less->fewer friends in his class now than he had last year.
L
21 tháng 12 2021
1. They usually have rice and fish
2. What are they having now?
3. They are having bottles of water and pizza with chicken now.
4. Can I have a glass of water?
5. I never have soup for dinner
6. She rarely has porridge for lunch
21 tháng 12 2021
1. They usually have rice and fish
2. What are they having now?
3. They are having bottles of water and pizza with chicken now.
4. Can I have a glass of water?
5. I never have soup for dinner
6. She rarely has porridge for lunch
= 2
= 4
= 6
Hk tốt
kb nhé
1 + 1 = 2
2 + 2 = 4
3 + 3 =6 NHA