1+3+5+...+(2x+1)=441

Số số hạng là \(\dfrac{2x+1-1}{2}+1=\dfrac{2x}{2}+1=x+1\left(số\right)\)

Tổng của dãy số là \(\left(2x+1+1\right)\cdot\dfrac{\left(x+1\right)}{2}=\left(x+1\right)^2\)

Do đó, ta có phương trình:

\(\left(x+1\right)^2=441\)

=>\(\left(x+1\right)^2-21^2=0\)

=>(x+1+21)(x+1-21)=0

=>(x+22)(x-20)=0

=>\(\left[{}\begin{matrix}x=-22\\x=20\end{matrix}\right.\)

Tổng: 1 + 3 + 5 + ... + (2x + 1) 

Số lượng số hạng là:

(2x + 1 - 1) : 2 + 1 = x + 1 (số hạng)

=> 1 + 3 + 5 + ... + (2x + 1) = (2x + 1 + 1) x (x + 1) : 2 = `(x+1)^2` 

=> \(\left(x+1\right)^2=441\)

\(=>\left(x+1\right)^2=21^2\\ TH1:x+1=21\\ =>x=21-1\\ =>x=20\\ TH2:x+1=-21\\ =>x=-21-1\\ =>x=-20\)

Mà: x > 0 => x = 20 

(2x+1)+(4x+2)+...+(400x+200)

\(=\left(2x+1\right)+2\left(2x+1\right)+...+200\left(2x+1\right)\)

\(=\left(2x+1\right)\left(1+2+...+200\right)\)

\(=\left(2x+1\right)\cdot\dfrac{200\left(200+1\right)}{2}=20100\left(2x+1\right)\)

Em cần làm gì với biểu thức này vậy?

Để A nguyên thì \(2024⋮x-2\)

=>\(x-2\in\){1;-1;2;-2;4;-4;8;-8;11;-11;22;-22;23;-23;44;-44;46;-46;88;-88;92;-92;184;-184;253;-253;506;-506;1012;-1012;2024;-2024}

=>x\(\in\){3;1;4;0;6;-2;10;-6;13;-9;24;-20;25;-21;46;-42;48;-44;90;-86;94;-90;186;-182;255;-251;508;-504;1014;-1010;2026;-2022}

Theo bài ra ta có: \(\left\{{}\begin{matrix}86-11⋮a\\142-27⋮a\end{matrix}\right.\)⇒ \(\left\{{}\begin{matrix}75⋮a\\115⋮a\end{matrix}\right.\) ⇒ a \(\in\) ƯC(75; 115)

 75 =  3.5²; 115 =  5.23 ⇒ ƯCLN(75; 115) = 5

⇒ a \(\in\) Ư(5) = {1; 5}

vì a > 27 nên không có giá trị nào của a thỏa mãn đề bài

Yesterday was a busy and fulfilling day for me. In the morning, I woke up early at around 7 AM and started my day with a jog through the park near my house. The crisp air and the sound of chirping birds made me feel refreshed. After my run, I went back home to have breakfast with my family. We enjoyed a hearty meal together, sharing stories and laughter.

In the late morning, I met up with a few friends at a local café. We spent a couple of hours catching up and chatting about our recent experiences. While we were there, I noticed other groups of people engaging in lively conversations and enjoying their coffee. The café was bustling with energy, which made the atmosphere even more enjoyable.

In the afternoon, I visited a museum with my cousin. We spent a few hours exploring the exhibits and learning about historical artifacts. It was both educational and interesting, and we took plenty of photos to remember the visit. 

By the evening, I felt a bit tired but content. I returned home, had a light dinner, and spent the rest of the night relaxing while watching a movie. Overall, it was a day filled with enjoyable activities, meaningful interactions, and a sense of accomplishment.

nghĩa là: tạo câu hỏi bằng cách sử dụng hiện tại đơn. Sau đó viết những câu trả lời ngắn về nó 

does she watch tv every day?

yes, she watches tv every day, and she watches cartoons every night,She watches cooking shows every morning

bạn cứ trả lời về chính bản thân bạn í

còn đây câu trả lời của tớ

I live in Vietnam 

my house has 5 rooms

bedroom is room i like best , because in my best room has many dolls

1.he is listening 

2.rains

3.is working , isn't working

4.is running,wants

5. speaks,comes

6.is coming , are meeting

1. Where's John? He _____is listening___(listen) to a new CD in his room.

2. Don't forget to take your umbrella with you to London. You know it always _____rains___(rain) in England.

3. Jean ____works____(work) hard all day but she ___is not working_____(not work) at the moment.

4. Look! That boy _____is running___ (run) after the bus. He____wants____(want) to catch it.

5. He _____speaks___(speak) German so well because he ____comes____(come) from Germany.

6. Shh! The boss ____is coming____(come). We ___will meet_____(meet) him in an hour and nothing is ready!

7. _____Do__you usually ____go___(go) away for Christmas or__Do_____ you ___stay___(stay) at home?

8. She _____is holding___(hold) some roses. They____smell____(smell) lovely.

9. Oh no! Look! It ____is snowing____(snow) again. It always___snows_____(snow) in this country.

10. Mary _____swims___ (swim) very well, but she ___doesn't run_____(not run) very fast.