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1. There’s the lady. Her dog was killed.
There’s the lady whose dog was killed.
2. That’s the man. He’s going to buy the company.
That’s the man who is going to buy the company
3. He’s the person. His car was stolen.
He’s the person whose car was stolen
4. She’s the new doctor.The doctor’s coming to the hospital next week.
She's the new doctor who is coming to the hospital next week
5. She’s the journalist. Her article was on the front page of The Times.
She's the journalist whose article was on the front page of The Times.
6. They’re the people. Their shop burned down last week.
They’re the people whose shop burned down last week
7. That’s the boy. He’s just got a place at university.
That’s the boy who has just got a place at university.
1. This is the man I met in Paris.
2. I wanted the painting you bought.
3. This is the chair my parents gave to me
4. She’s the woman who telephoned the police.
5. He’s the person who wanted to buy your house.
6. We threw out the computer which never worked properly.
7. This is the lion being ill recently.
8. The man driving the car was badly injured.
9. The children living in the next street broke the window.
10. That’s the woman I was telling you about.
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6 How often does your grandfather often listen to the radio
7 How often do you go to the gym
8 What did they send
9 What time did he leave the party
10 Where did he go
11 Who did he meet for coffee
12 Why did she called the firemen
13 How did he go to school
14 What does lan like doing
15 Where was your father last months
16 How much is the dictionary
17 How long did it take to finish the composition
18 Who bought a poster
What did Mrs Robinson by
19 Where is a restaurant
20 What did her neighbor give her
21 How was the homework yesterday
22 Do you have magaazine and newspapers
23 How often do you go to the movies
Bạn kiểm tra lại đề bài câu a, n=1 thì VT=1, VP=-1, nếu đề bài đúng thì vp phải là \(\dfrac{-\left(1\right)^{n-1}n\left(n+1\right)}{2}\)
\(n=1\Rightarrow VT=1=VP\)
Vậy mệnh đề đúng với n=1
Giả sử mệnh đề cũng đúng với \(n=k\left(k\in N\right)\), hay:
\(1^2-2^2+...+\left(-1\right)^{k-1}.k^2=\dfrac{\left(-1\right)^{k-1}.k.\left(k+1\right)}{2}\)
Ta cần chứng minh mệnh đề cũng đúng với \(n=k+1\) ,hay:
\(1^2-2^2+...+\left(-1\right)^{k-1}.k^2+\left(-1\right)^k.\left(k+1\right)^2=\dfrac{\left(-1\right)^k.\left(k+1\right)\left(k+2\right)}{2}\)
That vay:
\(VT=\dfrac{\left(-1\right)^{k-1}k\left(k+1\right)}{2}+\left(-1\right)^k.\left(k+1\right)^2=\dfrac{\left(-1\right)^{k-1}.k.\left(k+1\right)+2\left(-1\right)^k\left(k+1\right)^2}{2}\)
\(=\dfrac{\left(-1\right)^k\left(k+1\right)\left(-k+2k+2\right)}{2}=\dfrac{\left(-1\right)^k\left(k+1\right)\left(k+2\right)}{2}=VP\)
Vậy mệnh đề đúng với \(\forall n\in N\)
b/ \(n=7\Rightarrow VT=3^7=2187< 7!=5040\)
Vậy mệnh đề đúng với n=7
Giả sử mệnh đề đúng với \(n=k\left(k\in N;k\ge7\right)\),hay:
\(3^k\le k!\)
Ta cần chứng minh mệnh đề cũng đúng với \(n=k+1\) ,hay:
\(3^{k+1}\le\left(k+1\right)!\)
That vay:
\(3^k.3\le\left(k+1\right).k!\)
\(k>6\Rightarrow k+1>6\Rightarrow k+1>3\)
Ma \(3^k\le k!\)
\(\Rightarrow3^k.3\le\left(k+1\right).k!\Leftrightarrow3^{k+1}\le\left(k+1\right)!\)
Vậy mệnh đề đúng với \(\forall n\in N;n>6\)
\(...\Leftrightarrow2019\left(x-1\right)^2+2020\left(y+1\right)^2=0\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)