k cho mình nhé

4n-5 chia hết n+1

Suy ra 4.(n+1)-9 chia hết cho n+1.Suy ra 4.(n+1) chia hết cho n+1

Suy ra 9 chia hết cho n+1

Suy ra n+1 thuộc ước của 9={1,-1,3,-3,9,-9}

Suy ra n thuộc{0,-2,2,-4,8,-10}

Tham khảo bài này nha ! 

n + 2 \(⋮\) n - 3 

\(\Rightarrow\)( n - 3 ) + 5 \(⋮\) n - 3 

Mà: n - 3 \(⋮\) n - 3 

\(\Rightarrow\)5 \(⋮\) n - 3 

\(\Rightarrow\)n - 3 \(\in\) Ư (5) = { -1 , -5 , 1 , 5 } 

Ta có bảng : 

n - 3       -1        -5         1          5 

   n          2         -2         4          8

a) \(\frac{-6}{35}.\frac{-49}{60}=\frac{\left(-6\right).\left(-49\right)}{35.60}=\frac{\left(-6\right).\left(-7\right).\left(-7\right)}{\left(-5\right).\left(-7\right).\left(-6\right).\left(-10\right)}=\frac{-7}{\left(-5\right).\left(-10\right)}=\frac{-7}{50}\)

b) \(\frac{-16}{25}.\frac{-5}{24}=\frac{\left(-16\right).\left(-5\right)}{25.24}=\frac{\left(-8\right).2.\left(-5\right)}{\left(-5\right).\left(-5\right).\left(-8\right).\left(-3\right)}=\frac{2}{\left(-5\right).\left(-3\right)}=\frac{2}{15}\)

c) \(\frac{15}{-17}.\frac{5}{18}=\frac{15.5}{\left(-17\right).18}=\frac{5.3.5}{\left(-17\right).3.6}=\frac{5.5}{\left(-17\right).6}=\frac{25}{-102}\)

a) \(\frac{-6}{35}\cdot\frac{-49}{60}\)

\(=\frac{\left(-6\right)\cdot\left(-49\right)}{35\cdot60}\)

\(=\frac{294}{2100}=\frac{7}{50}\)

b)\(\frac{-16}{25}\cdot\frac{-5}{24}\)

\(=\frac{\left(-16\right)\cdot\left(-5\right)}{25\cdot24}\)

\(=\frac{80}{600}=\frac{2}{15}\)

c)\(\frac{15}{-17}\cdot\frac{5}{18}\)

\(=\frac{15\cdot5}{\left(-17\right)\cdot18}\)

\(=\frac{75}{-306}=\frac{25}{-102}\)

Bài 1 : 

Ta có : 

\(B=\frac{2010+2011}{2011+2012}=\frac{2010}{2011+2012}+\frac{2011}{2011+2012}\)

Vì : 

\(\frac{2010}{2011}>\frac{2010}{2011+2012}\)

\(\frac{2011}{2012}>\frac{2011}{2011+2012}\)

Nên : \(\frac{2010}{2011}+\frac{2011}{2012}>\frac{2010+2011}{2011+2012}\)

Vậy \(A>B\)

Bài 2 : 

\(\frac{n+1}{n-1}=\frac{n-1+2}{n-1}=\frac{n-1}{n-1}+\frac{2}{n-1}=1+\frac{2}{n-1}\)

\(\Rightarrow\)\(2⋮\left(n-1\right)\)

\(\Rightarrow\)\(\left(n-1\right)\inƯ\left(2\right)\)

Mà \(Ư\left(2\right)=\left\{1;-1;2;-2\right\}\)

Suy ra : 

Vì n là số tự nhiên nên \(n\in\left\{0;2;3\right\}\)

Vậy \(n\in\left\{0;2;3\right\}\)

\(\frac{19}{57}=\frac{19:19}{57:19}=\frac{1}{3}\)

\(\frac{19}{57}\) = \(\frac{1}{3}\)

rút gọn cho 19 

nhé bạn !!!!!!!!!!!

a ) CM : S < 1

Ta có : 

6 /15> 6/30                  

6 /16> 6/30 

6/17 > 6/30 

6/18 > 6/30

6/19 > 6 / 30 

=>     S = 6/15 + 6/16 + 6/17 + 6/18 + 6/19 > 6/30 x 5 = 1 

=>     S > 1 ( 1 ) 

CM :           S < 2 

6/16 < 6/15 , 6/17 < 6/15 , 6/18 < 6/15 , 6/19 < 6/15

=>      S = 6/15 + 6/16+ 6/17 + 6/18 + 6/19 < 6/15 x 5 = 2 

=>      S < 2 ( 2 )

Từ ( 1 ) , ( 2 ) =>                1 < S < 2 

b )    Do 1 < S < 2  => S ko phải STN
Chúc học giỏi !!! 

\(S=\frac{6}{15}+\frac{6}{16}+\frac{6}{17}+\frac{6}{18}+\frac{6}{19}>\frac{6}{20}+\frac{6}{20}+\frac{6}{20}+\frac{6}{20}+\frac{6}{20}\)

\(S>\frac{6}{20}\cdot5=\frac{30}{20}\)

\(\Rightarrow S>\frac{3}{2}>1\)

\(S< \frac{6}{14}+\frac{6}{14}+\frac{6}{14}+\frac{6}{14}+\frac{6}{14}\)

\(S< \frac{6}{14}\cdot5=\frac{30}{14}\)

\(S< \frac{15}{7}\Rightarrow S< \frac{14}{7}+\frac{1}{7}\)

\(S< 2+\frac{1}{7}\)

\(\Rightarrow1< \frac{3}{2}< S< 2< 2+\frac{1}{7}\)

\(\Leftrightarrow1< S< 2\Rightarrow S\notin Z\)

ko hiểu lắm

a) \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{2017\cdot2018}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)

\(=1-\frac{1}{2018}\)

\(=\frac{2017}{2018}\)

b) \(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{97\cdot99}\)( sửa 91.99 thành 97.99 mới đúng nha )

\(=\frac{1}{2}\left(\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...+\frac{2}{97}-\frac{2}{99}\right)\)

\(=\frac{1}{2}\left(\frac{2}{3}-\frac{2}{99}\right)\)

\(=\frac{1}{2}.\frac{64}{99}\)

\(=\frac{32}{99}\)

a) 1/1.2 + 1/2.3 + 1/3.4 +...+1/2017.2018

= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ....+1/2017 - 1/2018

= 1 - 1/2018 

= 2017/2018