Lời giải:

$BCNN(m,n) = 2^4.3^5.5.7^6.11^4$

\(\overline{ab}+\overline{ba}=187\)

\(\Rightarrow10a+b+10b+a=187\)

\(\Rightarrow11a+11b=187\)

\(\Rightarrow11\left(a+b\right)=187\)

\(\Rightarrow a+b=187:11=17\)

Mà \(0< a,b\le9\) nên \(\overline{ab}\in\left\{98;89\right\}\)

Ko có số nào có 2 chữ số chia hết cho 1 000 000 000 cả 

This morning is the first day of winter. I woke up early to look at the streets on a special day like this.

The big road runs across the front of my house, so from the balcony, I can see the entire street. It was only 6 a.m., it was still early, so the streets were deserted. It was just dawn, the corner of the horizon was pink, a rare pearl was slowly rising. The sky is heavy, gray, filled with gray and white clouds. The air is cold, dry, with cold winds blowing intermittently. The wind blew through the rows of crocodile trees on both sides of the sidewalk, causing the leaves to droop because of the cold. The wind blows dry leaves and trash from the sidewalk into every corner. At this time, the street lights were still lit, the weak yellow light had difficulty penetrating the thick fog. I can only see the houses near me, but the end of the road is blurry. About 30 minutes later, the sky was bright. On a winter day, it will not be sunny and a bit gloomy. Shops on both sides of the street began to open to welcome customers. Pushcarts selling breakfast sticky rice, dumplings, bread and coffee also stand scattered along the road. From the small alleys, the stream of people also poured out more and more. Everyone wore thick, tight scarves to avoid the cold. People walking on the sidewalk put their hands in their pockets, their heads bowed low, to avoid the cold wind. Maybe because it's cold, the stores aren't too crowded. People are more interested in hot porridge dishes with fragrant smoke. Until it was completely bright, I still couldn't hear the little bird singing like every other day. Maybe it's because it's too cold, so my whole family is already on winter break.

The street on an early winter morning was deserted and boring, but still gave me interesting and different feelings. I really like those moments of peace and relaxation.

tk

This morning is the first day of winter. I woke up early to look at the streets on a special day like this.

The big road runs across the front of my house, so from the balcony, I can see the entire street. It was only 6 a.m., it was still early, so the streets were deserted. It was just dawn, the corner of the horizon was pink, a rare pearl was slowly rising. The sky is heavy, gray, filled with gray and white clouds. The air is cold, dry, with cold winds blowing intermittently. The wind blew through the rows of crocodile trees on both sides of the sidewalk, causing the leaves to droop because of the cold. The wind blows dry leaves and trash from the sidewalk into every corner. At this time, the street lights were still lit, the weak yellow light had difficulty penetrating the thick fog. I can only see the houses near me, but the end of the road is blurry. About 30 minutes later, the sky was bright. On a winter day, it will not be sunny and a bit gloomy. Shops on both sides of the street began to open to welcome customers. Pushcarts selling breakfast sticky rice, dumplings, bread and coffee also stand scattered along the road. From the small alleys, the stream of people also poured out more and more. Everyone wore thick, tight scarves to avoid the cold. People walking on the sidewalk put their hands in their pockets, their heads bowed low, to avoid the cold wind. Maybe because it's cold, the stores aren't too crowded. People are more interested in hot porridge dishes with fragrant smoke. Until it was completely bright, I still couldn't hear the little bird singing like every other day. Maybe it's because it's too cold, so my whole family is already on winter break.

The street on an early winter morning was deserted and boring, but still gave me interesting and different feelings. I really like those moments of peace and relaxation.

A = \(\dfrac{8}{9}+\dfrac{24}{25}\) + \(\dfrac{48}{49}\) + ... + \(\dfrac{10200}{10201}\)

A = \(\dfrac{8}{3^2}\) + \(\dfrac{24}{5^2}\) + \(\dfrac{48}{7^2}\)  + ... + \(\dfrac{10200}{101^2}\)

Xét dãy số: 3; 5; 7;...; 101

Dãy số trên là dãy số cách đều với khoảng là: 5 - 3 = 2

Số số hạng của dãy số trên là: (101 - 3): 2 + 1 = 50

Vậy A có 50 hạng tử

     \(\dfrac{8}{9}\)  < \(1\)

     \(\dfrac{24}{25}\) < 1

    \(\dfrac{48}{49}\) < 1

  ..................

\(\dfrac{10200}{10201}\) < 1

Cộng vế với vế ta có: 

A = \(\dfrac{8}{9}\) + \(\dfrac{24}{25}\) + \(\dfrac{48}{49}\) +....+ \(\dfrac{10200}{10201}\) < 1 x 50

A < 50 < 99,75 (trái với đề bài)

Vậy việc chứng minh A > 99,75 là điều không thể xảy ra. 

đề bài chưa hoàn chỉnh thì khó đưa ra câu trả lời nha

\(A=\dfrac{1}{2\cdot6}+\dfrac{1}{3\cdot8}+...+\dfrac{1}{2023\cdot4048}\)

\(=\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+...+\dfrac{2}{4046\cdot4048}\)

\(=\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{4046}-\dfrac{1}{4048}\)

\(=\dfrac{1}{4}-\dfrac{1}{4048}=\dfrac{1011}{4048}\)

\(A=\frac{1}{2.6}+\frac{1}{3.8}+\frac{1}{4.10}+...+\frac{1}{2023.4048}\\=\frac12\left(\frac{2}{2.6}+\frac{2}{3.8}+\frac{2}{4.10}+...+\frac{2}{2023.4048}\right)\\=\frac12\left( \frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2023.2024}\right)\\=\frac12\left(\frac12-\frac13+\frac13-\frac14+\frac14-\frac15+...+\frac{1}{2023}-\frac{1}{2024}\right)\\=\frac12\left(\frac12-\frac{1}{2024}\right) \\=\frac12.\frac{1011}{2024}=\frac{1011}{4048}\)

During the summer holidays, I always make the most of the warm weather and free time. One of my favorite activities is spending time at the beach, feeling the soft sand between my toes and listening to the soothing sound of the waves crashing against the shore. I love swimming in the refreshing ocean and building sandcastles with my friends or family.

In addition to beach days, I enjoy going on hikes in nature reserves or national parks. The lush greenery, the chirping of birds, and the fresh air invigorate me as I explore the trails and take in the breathtaking views from the hilltops.

Summer holidays also give me the opportunity to catch up on reading. I love getting lost in a good book while lounging in a hammock or sitting under a shady tree. Whether it's a thrilling mystery, a heartwarming romance, or an inspiring autobiography, reading transports me to different worlds and broadens my perspective.

Furthermore, I often spend time with my friends during the summer holidays, whether it's going to outdoor concerts, having BBQs, or simply hanging out and having fun. These moments create lasting memories and strengthen our bonds. Overall, my summer holidays are filled with sun, sea, nature, books, and cherished moments with loved ones.

Khu phố của tôi râtd đông, đặc biệt là khoảng 9 - 11 giờ sáng sẽ có rất nhiều người qua lại, nhiều đến nỗi tôi không thể qua đường.

Khu phố nhà em là một khu phố tuy không rộng nhưng lại rất đẹp. Người dân ở đây sống rất ý thức, không xả rác bừa bãi ra môi trường. Khi em mới chuyển đến, em vô cùng thích sự văn minh, lịch sự của con người ở đó. Ở khu phố nhà em, cứ tối đến sau giờ ăn cơm các bạn sẽ sang nhà nhau và cùng học nhóm. Lớn giảng cho bé và cứ thế chúng em học đến 9 giờ rồi đi ngủ. Có những hôm khu phố còn tổ chưcs đi cắm trại nữa. Em yêu biết bao khu phố nhà em!

\(5:\dfrac{3}{14}-4\dfrac{4}{5}:\dfrac{3}{4}\\ =5.\dfrac{14}{3}-\dfrac{24}{5}.\dfrac{4}{3}\\ =\dfrac{70}{3}-\dfrac{32}{5}\\ =\dfrac{254}{15}\)

.

\(-\dfrac{13}{8}.\left(\dfrac{8}{13}+\dfrac{32}{38}\right)-\dfrac{15}{7}\\ =-\dfrac{13}{8}.\left(\dfrac{8}{13}+\dfrac{16}{19}\right)-\dfrac{15}{7}\\ =-\dfrac{13}{8}.\dfrac{360}{247}-\dfrac{15}{7}\\ =-\dfrac{45}{19}-\dfrac{15}{7}\\ =-\dfrac{600}{133}\)

\(\dfrac{x}{3}-\dfrac{1}{8}+\dfrac{4}{2}-\dfrac{3}{8}=\dfrac{5}{50}\\ \dfrac{x}{3}-\dfrac{4}{8}+2=\dfrac{1}{10}\\ \dfrac{x}{3}-\dfrac{1}{2}+2=\dfrac{1}{10}\\ \dfrac{x}{3}+\dfrac{3}{2}=\dfrac{1}{10}\\ \dfrac{x}{3}=\dfrac{1}{10}-\dfrac{3}{2}\\ \dfrac{x}{3}=-\dfrac{7}{5}\\ x=-\dfrac{7}{5}.3\\ x=-\dfrac{21}{5}\)