bạn ơi nhầm rồi đây là toán mừ

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Để tính S₁ + S₂ + S₃ + ... + S₂₀₁₃ ta tìm số lần xuất hiện chữ số 0; 1;2;...9 từ 000 đến 1999

+) Từ 000 đến 999: có 1000 số. mỗi số có 3 kí tự => có tất cả 3.1000 = 3000 kí tự

trong đó số lần xuất hiện các kí tự 0;1;2;..;9 như nhau

=>Mỗi  Số 0;1;...;9 xuất hiện 3000 : 10 = 300 lần

+) Từ 1000 đến 1999: Theo trên , ta có Mỗi số 0;2;3;..;9 cũng xuất hiện 300 lần

riêng số 1 xuất hiện 300 + 1000 = 1300 lần (Do tính số 1 đứng ở hàng nghìn)

Vậy Từ từ 000 đến 1999 : số 1 xuất hiện 1600 lần; các số 0;;2;3;...;9 đều xuất hiện 600 lần

+) từ 2000 đến 2013 có:

S₂₀₀₀ + ...+ S₂₀₀₉ = (2+ 0+ 0 + 0) + (2+0+0+1)...+(2+0+0+9)+(2+0+1+0) +(2+0+1+1)+(2+0+1+2) +(2+0+1+3)

= 2.14 + (1+2+3+..+9) + 1+2+3+4 = 28 + 45 + 10 = 83

Vậy S₁ + S₂ + S₃ + ... + S₂₀₁₃ = 1600 .1 + 600. (0+ 2+3+4+..+9) + 83 = 1600 + 600.44 + 83 = 28083

Để tính S₁ + S₂ + S₃ + ... + S₂₀₁₃ ta tìm số lần xuất hiện chữ số 0; 1;2;...9 từ 000 đến 1999

+) Từ 000 đến 999: có 1000 số. mỗi số có 3 kí tự => có tất cả 3.1000 = 3000 kí tự

trong đó số lần xuất hiện các kí tự 0;1;2;..;9 như nhau

=>Mỗi  Số 0;1;...;9 xuất hiện 3000 : 10 = 300 lần

+) Từ 1000 đến 1999: Theo trên , ta có Mỗi số 0;2;3;..;9 cũng xuất hiện 300 lần

riêng số 1 xuất hiện 300 + 1000 = 1300 lần (Do tính số 1 đứng ở hàng nghìn)

Vậy Từ từ 000 đến 1999 : số 1 xuất hiện 1600 lần; các số 0;;2;3;...;9 đều xuất hiện 600 lần

+) từ 2000 đến 2013 có:

S₂₀₀₀ + ...+ S₂₀₀₉ = (2+ 0+ 0 + 0) + (2+0+0+1)...+(2+0+0+9)+(2+0+1+0) +(2+0+1+1)+(2+0+1+2) +(2+0+1+3)

= 2.14 + (1+2+3+..+9) + 1+2+3+4 = 28 + 45 + 10 = 83

Vậy S₁ + S₂ + S₃ + ... + S₂₀₁₃ = 1600 .1 + 600. (0+ 2+3+4+..+9) + 83 = 1600 + 600.44 + 83 = 28083 **** ☺

ta có \(\frac{a}{1+b-a}+a\left(1+b-a\right)\ge2a\)hay \(\frac{a}{1+b-a}\ge a\left(1+a-b\right)=a\left(2a+c\right)\)

tương tự ta sẽ có :

\(\frac{a}{1+b-a}+\frac{b}{1+c-b}+\frac{c}{1+a-c}\ge2a^2+2b^2+2c^2+ab+ac+bc\)

\(\ge\frac{3}{2}\left(a^2+b^2+c^2\right)+\frac{1}{2}\left(a^2+b^2+c^2+2ab+2bc+2ac\right)\ge\frac{1}{2}\left(a+b+c\right)^2+\frac{1}{2}\left(a+b+c\right)^2\)

\(\ge\left(a+b+c\right)^2=1\)

vậy ta  có điều phải chứng minh

dấu bằng xảy ra khi \(a=b=c=\frac{1}{3}\)

vì bạn muốn làm bằng BDT Bunhia nên mình làm cách đó nhé : 

ta có : \(\left[a\left(1+b-a\right)+b\left(1+c-b\right)+c\left(1+a-c\right)\right]\left(\frac{a}{1+b-a}+\frac{b}{1+c-b}+\frac{c}{1+a-c}\right)\)

\(\ge\left(a+b+c\right)^2=1\) ( áp dụng Bunhia ) 

nên ta có : \(VT\ge\frac{1}{a\left(1+b-a\right)+b\left(1+c-b\right)+c\left(1+a-c\right)}=\frac{1}{a\left(2b+c\right)+b\left(2c+a\right)+c\left(2a+c\right)}\)

\(\ge\frac{1}{3\left(ab+bc+ca\right)}\) mà \(ab+bc+ca\le\frac{\left(a+b+c\right)^2}{3}=\frac{1}{3}\)

nên ta có : \(VT\ge\frac{1}{3\times\frac{1}{3}}=1=VP\) vậy ta có đpcm

Từ bất đẳng thức Cô si ta có:

\(4\left(ab+bc+ca\right)\left(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\right)\le\left[\frac{ab+bc+ca}{ca}+ca\left(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\right)\right]^2\)

\(\Rightarrow\)Ta cần chứng minh:

\(\frac{ab+bc+ca}{ca}+ca\left(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\right)\le\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}\)

Vì vai trò của a, b, c trong bất đẳng thức như nhau, nên không mất tính tổng quát ta giả sử \(a\ge b\ge c\)nên bất đẳng thức cuối cùng đùng. Vậy bất đẳng thức được chứng minh.

sai r bạn ơi ko biết còn đòi

Bài 1:

\(A=\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+...+1986}\right)\)

Nhận xét: \(1-\frac{1}{1+2+...+n}=1-\frac{2}{n\left(n+1\right)}=\frac{n^2+n-2}{n\left(n+1\right)}=\frac{\left(n-1\right)\left(n+2\right)}{n\left(n+1\right)}\)

Do đó: \(\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+...+1986}\right)\)

\(=\frac{1\cdot4}{2\cdot3}\cdot\frac{2\cdot5}{3\cdot4}\cdot...\cdot\frac{1985\cdot1988}{1986\cdot1987}=\frac{1\cdot4\cdot1988}{1986\cdot3}=\frac{3976}{2979}\)

Bài 2:

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)

\(\Rightarrow\frac{4\cdot4^5}{3\cdot3^5}\cdot\frac{6\cdot6^5}{2\cdot2^5}=2^x\)\(\Rightarrow\frac{4^6}{3^6}\cdot\frac{6^6}{2^6}=2^x\)

\(\Rightarrow\frac{\left(2^2\right)^6}{3^6}\cdot\frac{\left(2\cdot3\right)^6}{2^6}=2^x\)\(\Rightarrow\frac{2^{12}}{3^6}\cdot\frac{2^6\cdot3^6}{2^6}=2^x\)

\(\Rightarrow\frac{2^6\cdot3^6\cdot2^{12}}{2^6\cdot3^6}=2^x\)\(\Rightarrow2^{12}=2^x\Rightarrow x=12\)

đúng rồi đó bạn ks bạn ý đi chứ

\(\frac{3}{5}=\frac{24}{40};\frac{3}{8}=\frac{15}{40};\frac{3}{10}=\frac{12}{40};\frac{3}{2}=\frac{60}{40}\)

\(\frac{3}{5}=\frac{3\times8}{5\times8}=\frac{24}{40}\)

\(\frac{3}{8}=\frac{3\times5}{8\times5}=\frac{15}{40}\)

\(\frac{3}{10}=\frac{3\times4}{10\times4}=\frac{12}{40}\)

\(\frac{3}{2}=\frac{3\times20}{2\times20}=\frac{60}{40}\)

The Manager
745 Le Loi Rd
Sunflower Hotel Da Nang
610 Bach Dang Rd, Da Nang

20 March 2018

Dear Sir or Madam,

I am writing in response to your advertisement on Viet Nam Net for a young and enthusias receptionist.

Last summer, I worked as a receptionist in International hotel for 2 months. My responsibilities included greeting guests, giving them information and help them check in. I also took part in answering the phone as well as their questions.

I consider myself to be young, hardworking,enthusias and helpful. I can speak English quite good and can work as an interpreter. In addition, I can work for long hours, If required.

I can provide references from the hotel’s human resources department.

It would be grateful if I could visit your hotel and discuss my application with you in person. I am available for an interview on any day from Monday to Thursday.

If my application is accepted, I will be able to start work from 15th of May. I am enclosing my CV with this letter.

I look forward to hearing from you soon.

Yours faithfully,
Ichika

FROM: Hoai Giang

TO: The manager of Sunflower hotel

ADRESS: Number 310 Bach Dang St, Da Nang city

Dear sir,

I'm currently writing this letter in order to respond to your advertisement about inviting a receptionist for the sunflower hotel at Da Nang. I am pleased to have the job and serve as a receptionist. 

I've worked as a receptionist for 4 hotels 2 years before. My responsibilities in all the hotels include introducing to passengers, writing the information list ( including phone numbers, customer names and rooms ) and answering the phone. My salary wasn't high after it was overdue, but I shall be grateful to help. 

I've been learning English for over 10 years, so my abiliy is to speak English fluetly, please don't worry. I always consider myself to be hardworking, reliable and energe.

It is my pleasure to serve in this luxurious hotel. If my application is accepted, I will agree and try my best to work as a receptionist in this Sunflower hotel. I shall look forward and wait for your agreement. Please contact me if necessary, with my phone number **********

Your responder

Giang

Duong Hoai Giang.

mình trả lời chi bạn nè ! cả 3 bạn đều đạt giải đặc biệt

Ba bạn đó đều nêu ra các trường hợp về các giải nhất nhì ba nhưng đều không đúng 

Như thế là phải có giải đặc biệt rồi mà 3 bạn chọn trong 4 giải thì sẽ có 36 cách chọn

Nên khả năng chọn đúng là rất thấp

Do đó tốt muốn biết chính xác thì phải hỏi cô Phương nhé

My favorite idol of all time is Michael Jackson, and I believe that he is also an idol of many people all over the world. He appeared to be a star at a very young age, and his talent continued to shine brightly through time. In his early 20s, he officially started his individual singing career and became one of the legends of the music industry. Throughout his life, Michael had sold out more than 400 million music records and won many honorable awards. His name, music, dancing skills, personal life and information was the hottest subject for the mass media at that time. People could not stop talking about him, and it could be said that there was nobody that had not heard of Michael Jackson. He was not only a singer and professional dancer, but he was also a producer, musician, and actor. His light as a King of Pop was supposed to shine for many more decades, but there were many scandals that came to him a fierce flood had drown him to the bottom of the lake. He spent many of his last years to face charges as well as financial problems. In 2009, audiences had expected him to return in an international tour named This Is It, but an accident in wrong usage of medicines had taken his life in shock. People on over the world were informed about his death, and it was said that no one could ever replace his position to be the King of Pop. Although he had a lot of troubles in his life, people cannot deny the fact that he made many positive influences on the music industry. Michael Jackson had dedicated his life to art, and all of his effort will forever be remembered.

My favorite celebrity is Emma Watson. She is known for the movie Harry Potter series which she played the heroine. She was born on April, 15th, 1990, in Oxford England. She has brown big eyes and brunet hair. She is tall and thin. She is not only very beautiful and femininity but also very smart just the Hermione who is one of the role in Harry Potter and always gets good grades. She s to put on a play which is one of her dream when she was very young, now her dream came true and has an achievement .Most important of all, the reasons why I admire her are that her acting is masterly and her character is not cocky after became famous as an adolescent just us

HT.