\(F=\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+...+\dfrac{1}{18\cdot19\cdot20}\\ =\dfrac{1}{2}\left(\dfrac{2}{1\cdot2\cdot3}+\dfrac{2}{2\cdot3\cdot4}+...+\dfrac{2}{18\cdot19\cdot20}\right)\\ =\dfrac{1}{2}\left(\dfrac{3-1}{1\cdot2\cdot3}+\dfrac{4-2}{2\cdot3\cdot4}+...+\dfrac{20-18}{18\cdot19\cdot20}\right)\\ =\dfrac{1}{2}\left(\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+...+\dfrac{1}{18\cdot19}-\dfrac{1}{19\cdot20}\right)\\ =\dfrac{1}{2}\left(\dfrac{1}{1\cdot2}-\dfrac{1}{19\cdot20}\right)\\ =\dfrac{1}{2}\cdot\left(\dfrac{1}{2}-\dfrac{1}{380}\right)\\ =\dfrac{1}{2}\cdot\dfrac{189}{380}\\ =\dfrac{189}{760}\)

Số lượng số hạng là:

(188 - 3) : 5 + 1 = 38 (số hạng)

Tổng của dãy số là:
(188 + 3) x 38 : 2 = 3829 

ĐS: ...

Số số hạng của dãy số sau là : ( 188 - 3 ) : 5 + 1 = 38 ( số )

Tổng của dãy số trên là : ( 188 + 3 ) x 38 : 2 = 3629 ( số )

Đáp số : 3629 số

Đây nhé bạn

\(139\cdot43+139\cdot57\)

\(=139\cdot\left(43+57\right)\)

\(=139\cdot100=13900\)

13900

a: Bán kính mặt trăng là:

6370:4=1592,5(km)

Trong các số đo 1200km;1740km;2100km thì 1740km gần với 1592,5km nhất

nên bán kính Mặt Trăng là 1740km

b: Khoảng cách từ Mặt Trăng đến Trái Đất là:

\(3\cdot2\cdot6370=38220\left(km\right)\)

trong các số ,  , 

Khoảng cách từ Mặt Trăng đến Trái Đất là 191000km

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.