\(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}=\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}\)

Đặt A= \(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

=\(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{99}+\dfrac{1}{100}\right)-2\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)\)

=\(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{99}+\dfrac{1}{100}\right)-\left(1+\dfrac{1}{2}+...+\dfrac{1}{50}\right)\)

= \(\left(\dfrac{1}{51}+\dfrac{1}{52}+\dfrac{1}{53}+...+\dfrac{1}{100}\right)\)

Is there anything to drink? I’m very thirsty.

They're farmers. They work on a farm.

Trong các số đã cho ít nhất có một số dương vì nếu tất cả đều là số âm thì tổng của 5 số bất kì sẽ là số âm (loại)

Tách riêng các số dương đó còn 30 số xếp thành 6 nhóm mỗi nhóm có 5 số

Ta có tổng của 5 số bất kì là số dương nên tổng của 6 nhóm đều là số dương

\(\Rightarrow\) tổng của 31 số đó là số dương

1. How old Hoa will be on her next brithday ?

\(\Rightarrow\) will Hoa

2. Would you like seeing a movie with me tonight?

\(\Rightarrow\) to see

3. Nga's birthday is in the ninth of March

\(\Rightarrow\)on

4.We don't will have a party next Friday

\(\Rightarrow\) won't

5. Today is Thursday, the two of November

\(\Rightarrow\) second

6. Hoa doesn't have a lots of friends in her school

\(\Rightarrow\) any

7. What are your telephone number, Nga

\(\Rightarrow\) is

8. Mai will goes to Hai Phong tomorrow afternoon

\(\Rightarrow\) go

9. Who are you and your friends talk about ?

\(\Rightarrow\) talking

10. Linh lives with her uncle on 73 Nguyen Trai street

\(\Rightarrow\) at

Among my favourite sports and hobbies, I like swimming the best for several reasons. Firstly, I think playing in the water could bring great joy. It also helps reduce stress and I always feel refreshed and relaxed after swimming for about half an hour. Secondly, swimming is an excellent way to keep myself fit and healthy. It helps build up my muscle strength and prevent many heart and lung diseases. Finally, besides being a great sport, swimming is also an important survival skill, because without knowing how to swim well, it could be dangerous if there is a flood, or simply if we want to play near bodies of water. Many of such accidents have occured to teenagers lately. In conclusion, swimming will always be my preferred hobby because it is not only healthy and fun but also a life-saving skill.

2,(18)=2+0,(18)=2+0,(01).18=2+1/99.18=2+2/11=24/11

Vì \(\dfrac{-2}{x}=\dfrac{y}{6}\)

\(\Rightarrow xy=-2.6\)

\(\Rightarrow xy=-12\)

Mà x<0<y

\(\Rightarrow\) x \(\in\) {-1;-2;-3;-4;-6;-12}

\(\Rightarrow\) y \(\in\) {12; 6; 4; 3; 2; 1}

Vậy (x,y)=(-1,12);(-2;6);(-3;4);(-4;3);(-6;2);(-12;1) thỏa mãn bài ra

\(7^2.49^3.7^7\)

= \(7^7.\left(7^2\right)^3.7^7\)

= \(7^7.7^6.7^7\)

= \(7^{7+6+7}\)
= \(7^{20}\)

\(3^5.9^4.27^2.81\)

= \(3^5.\left(3^2\right)^4.27^2.81\)

= \(3^2.3^8.\left(3^6\right)^2.3^3\)

= \(3^2.3^8.3^{12}.3^3\)

= \(3^{2+8+12+3}\)

= \(3^{25}\)

Is there a telephone I can use ?