a) Để \(\frac{7}{n+1}\) đạt giá trị nguyên

<=> 7 \(⋮\) ( n + 1 )

=> n + 1 \(\in\) Ư(7) = { - 7 ; -1 ; 1 ; 7 }

=> n \(\in\) { -8 ; -2 ; 0 ; 6 }

b) Để \(\frac{n+5}{n-2}\) đạt giá trị nguyên

<=> \(n+5⋮n-2\)

=> ( n - 2 ) + 7 \(⋮\) n - 2

=> 7 \(⋮\) n - 2

=> n -  2 \(\in\) Ư(7) = { - 7 ; - 1 ; 1 ; 7 }

=> n \(\in\) { - 5 ; 1 ; 3 ; 9 }

c) Để \(\frac{4n-1}{n-3}\) đạt giá trị nguyên

<=> 4n-1 \(⋮\) n - 3

=> ( 4n - 12 ) + 11 \(⋮\) n- 3

=> 4(n-3) + 11 \(⋮\) n - 3

=> 11 \(⋮\)n  - 3

=> n - 3 \(\in\) Ư(11) = { - 11 ; - 1 ; 1 ; 11}

=> n \(\in\) { - 8 ; 2 ; 4 ; 14 }

k thấy chụp đứng ik

Trả lời:

\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right)\left(5x+6\right)}=\frac{2005}{2006}\)

\(\Rightarrow1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(\Rightarrow1-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(\Rightarrow\frac{1}{5x+6}=1-\frac{2005}{2006}\)

\(\Rightarrow\frac{1}{5x+6}=\frac{1}{2006}\)

\(\Rightarrow5x+6=2006\)

\(\Rightarrow5x=2000\)

\(\Rightarrow x=400\)

Vậy x = 400

Trả lời:

\(\frac{x}{2008}-\frac{1}{10}-\frac{1}{15}-\frac{1}{21}-...-\frac{1}{120}=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}-\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right)=\frac{5}{8}\)\(\frac{5}{8}\)

Đặt \(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\), ta được : \(\frac{x}{2008}-A=\frac{5}{8}\) (*)

\(\Rightarrow A=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(\Rightarrow A=2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)

\(\Rightarrow A=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)

\(\Rightarrow A=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(\Rightarrow A=2\left(\frac{1}{4}-\frac{1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)

Thay A vào (*) , ta có: 

\(\frac{x}{2008}-\frac{3}{8}=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}=1\)

\(\Rightarrow x=2008\)

Vậy x = 2008 

e,\(3\frac{2}{7}x-\frac{1}{8}=2\frac{3}{4}\)

\(=>\frac{23}{7}x-\frac{1}{8}=\frac{11}{4}\)

\(=>\frac{23}{7}x=\frac{11}{4}+\frac{1}{8}=\frac{23}{8}\)

\(=>x=\frac{23}{8}:\frac{23}{7}\)

\(=>x=\frac{7}{8}\)

b) 5 và 4/7 :x=13

  39/7 :x =13

          x= 39/7 :13

         x= 3/7

đây nhá có gì thắc mắc hỏi chị nhá

b) \(5\frac{1}{4}.\frac{3}{8}+10\frac{3}{4}.\frac{3}{8}\)

\(=\left(5\frac{1}{4}+10\frac{3}{4}\right).\frac{3}{8}\)

\(=16.\frac{3}{8}=6\)

c) \(6\frac{1}{5}.\frac{-2}{7}+14\frac{4}{5}.\frac{-2}{7}\)

\(=\left(6\frac{1}{5}+14\frac{4}{5}\right).\frac{-2}{7}\)

\(=21.\frac{-2}{7}=-6\)

sao thi muộn vậy bn ! mk thi xong lâu rùi

bài 7:

(9:9)+(9-9)+9=10

(9+9)-9+(9:9)=10

9x9:9+(9:9)=10

bài 9 

76 + 8 + 5 + 9 + 2 - 4 + 3  + 1 = 100 

nha bạn