\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{63}+...+\frac{1}{\left(x+1\right)\left(x+4\right)}=\frac{199}{400}\)(ĐK \(x\ne-1;-4\))

=> \(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{\left(x+1\right)\left(x+4\right)}=\frac{199}{400}\)

=> \(\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{\left(x+1\right)\left(x+4\right)}\right)=\frac{199}{400}\)

=> \(\frac{1}{2}\left(1-\frac{1}{x+4}\right)=\frac{199}{400}\)

=> \(1-\frac{1}{x+4}=\frac{199}{400}:\frac{1}{2}=\frac{199}{200}\)

=> \(\frac{1}{x+4}=1-\frac{199}{200}=\frac{1}{200}\)

=> x + 4 = 200 => x = 196(tm)

Ta có 

1/3 = 1/1 x 3

1/15 = 1/3 x 5

1/35 = 1/5 x 7

.....

1/(x + 1 ) x ( x + 4 )

\(\Rightarrow\)1 - 1/3 + 1/3 - 1/5 +1/5 - 1/7 +............+ 1/( x + 1 ) - 1/( x + 4) = 199/400

\(\Rightarrow\)1 - 1/( x + 4 ) = 199/400

\(\Rightarrow\)1/(x + 4 ) = 1 - 199/400

\(\Rightarrow\)1/(x + 4 ) = 201/400

còn lại bạn tự làm nha

Bài của mình bị thiếu 1 trường hợp nên bạn tham khảo bài của bạn kia nhé. :<<

\(\left(1-x\right)^2-1\frac{3}{9}=1\frac{4}{9}\)

=> \(\left(1-x\right)^2=1\frac{4}{9}+1\frac{3}{9}=\frac{25}{9}\)

=> \(\left(1-x\right)^2=\left(\frac{5}{3}\right)^2\)

=> \(\orbr{\begin{cases}1-x=\frac{5}{3}\\1-x=-\frac{5}{3}\end{cases}}\)

=> \(\orbr{\begin{cases}x=-\frac{2}{3}\\x=\frac{8}{3}\end{cases}}\)

ĐK : x \(\ne\)0 ; \(x\ne-4\)

Ta có : \(\frac{1}{5}+\frac{1}{45}+\frac{1}{117}+...+\frac{1}{x\left(x+4\right)}=\frac{53}{216}\)

\(\Rightarrow\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{x\left(x+4\right)}=\frac{53}{216}\)

=> \(\frac{1}{4}.\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{x\left(x+4\right)}\right)=\frac{53}{216}\)

=> \(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{x}-\frac{1}{x+4}=\frac{53}{216}:\frac{1}{4}\)

=> \(1-\frac{1}{x+4}=\frac{53}{54}\)

=> \(\frac{1}{x+4}=\frac{1}{54}\)

=> x + 4 = 54

=> x = 50 (tm)

Vậy x = 50

\(a)\frac{5}{6}+\left(\frac{-1}{2}\right)+\frac{3}{4}\)

\(=\frac{1}{3}+\frac{3}{4}\)

\(=\frac{13}{12}\)

\(b)\left(0,75-\frac{1}{3}\right):\frac{7}{15}\)

\(=\left(\frac{3}{4}-\frac{1}{3}\right).\frac{15}{7}\)

\(=\frac{5}{12}.\frac{15}{7}\)

\(=\frac{25}{28}\)

\(c)\frac{7}{12}-\frac{3}{4}.\frac{5}{6}\)

\(=\frac{7}{12}-\frac{5}{8}\)

\(=\frac{-1}{24}\)

\(d)\left(2\frac{1}{3}+1\frac{3}{4}\right).\frac{12}{13}\)

\(=\left(\frac{7}{3}+\frac{7}{4}\right).\frac{12}{13}\)

\(=\frac{49}{12}.\frac{12}{13}\)

\(=\frac{49}{13}\)

a)\(\frac{5}{6}+\frac{-1}{2}+\frac{3}{4}=\frac{10}{12}-\frac{6}{12}+\frac{9}{12}=\frac{10-6+9}{12}=\frac{13}{12}\)

b)\(\left\{0,75-\frac{1}{3}\right\}:\frac{7}{15}=\left\{\frac{3}{4}-\frac{1}{3}\right\}.\frac{15}{7}=\left\{\frac{9}{12}-\frac{4}{12}\right\}.\frac{15}{7}=\frac{5}{12}.\frac{15}{7}=\frac{75}{84}\)

c)\(\frac{7}{12}-\frac{3}{4}.\frac{5}{6}=\frac{7}{12}-\frac{5}{8}=\frac{14}{24}-\frac{15}{24}=\frac{-1}{24}\)

d)\(\left\{2\frac{1}{3}+1\frac{3}{4}\right\}.\frac{12}{13}=\left\{\frac{7}{3}+\frac{7}{4}\right\}.\frac{12}{13}=\left\{\frac{28}{12}+\frac{21}{12}\right\}.\frac{12}{13}=\frac{39}{12}.\frac{12}{13}=3\)

a) Ta có x thuộc B(4)

=> B(4) = {0;4;8;12;16;20;24;28;32;36;40;44;48;52;56;60;...}

Mà 8 \(\le\)x \(\le\)57 => x \(\notin\){0;4;60}

Vậy x \(\in\){8;12;16;20;....;56}

b) Vì x \(⋮\)12 nên x \(\in\)B(12) = {0; 12 ; 24;36;48;60;72;84;96;108;...}

Mà \(0< x\le105\)nên x \(\in\){12;24;...;96}

cảm ơn bạn huỳnh quang sang ạ

1. you should take the bus to get to the department store.
2. it would be a good idea to go camping this weekend.
3. people will be surprise when they know Son Dong cave
4. Windsor Castle is one of the most beautiful castles in the world
5. there are a lot of school on my way to streets

Exercise: Rearrange the words to make sentences

1. store/ take/ departmant/ to/ bus/ You/ should/ get/ to/ the/ .

You should take to get to the department store .

2. would/ good/ camping/ It/ be/ a/ weekend/ idea/ to/ go/ this/ .

It would be a good idea to go camping this weekend.

3. will/ surprise/ when/ they/ People/ be/ know/ Son Doong/ cave/ . 

People will be surprise when they know Son Dong cave.

4. Winsor castle/ the/ beautiful/ is/ word/ The/ one/ most/ of/ castle/ in/ the/ .

Winsor castle is one of the most beautiful castle in the world .

5. There/ my/ a/ trees/ lot/ school/ on/ to/ are/ way/ of/ . 

There are alot of trees on my way to school

\(7^{n+4}-7^n=7^n.7^4-7^n=7^n.\left(7^4-1\right)=7^n.2400\) chia hết cho 30

\(=125+\left(81+4\right).2+\left(27-3\right):4\)

\(=125+85.2+\left(27-3\right):4\)

\(=125+85.2+24:4\)

\(=125+170+24:4\)

\(=125+170+6\)

\(=295+6\)

\(=301\)

Ta có :

= 2.[1/10.12+1/12.14+1/14.16+...+1/x.(x+2)] = 19/400 = 2/10.12+2/12.14+2/14.16+...+2/x.(x+2) = 19/400

Mà 2/10.12=1/10-1/12

      2/12.14=1/12-1/14

............................................

= 1/10-1/12+1/12-1/14+...+1/x-1/x+2 = 19/400

= 1/10-1/x+2 = 19/400

=>1/x+2 = 1/10-19/400 => 1/x+2=21/400

Đừng ghi ngắn quá, giải thik giùm mk lun nha!!!

45-5(x-23)=15

5(x-23)=45-15

5(x-23)=30

(x-23)=30:5

(x-23)=6

x=6+23

x=29

vậy x=29