a, \(\left(-28\right)+82=82-26=56\)

b, \(51+\left(-97\right)=51-97=-46\)

bạn Hoàng Lan ơi bạn làm đúng rồi

Ta thấy 12 ; 16 ; 24 đều là số chẵn

Nên có thể chia cho mỗi em 2;4;6;8 cây bút , quyển vở ,24 cây bút

Thì mỗi em đều 8 ; 3 ; 3

TL :

120 : 54 - [ 50 : 2 - 3² - 2 x 4 ]

120 : 54 - [ 50 : 2 - 9 - 8 ]

120 : 54 - [ 25 - 1 ]

120 : 54 - 24

120 : 30

4

3n+1 chia hết cho 11-n.Vì 3(11 - n) chia hết cho 11 - n

3(11 - n) + (3n + 1) chia hết cho 11 - n

33 - 3n + 3n + 1 chia hết cho 11 - n

34 chia hết cho 11 - n

11 - n thuộc Ư(34)

11 - n thuộc {±1; ±2; ± 17; ±34}

 n thuộc {45; 28; 13; 12; 10; 9; -6; -23}

3n+1chia hết 11-n

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{\left(2n-2\right)2n}\)

\(=\frac{1}{2}.\frac{2}{2.4}+\frac{1}{2}.\frac{2}{4.6}+\frac{1}{2}.\frac{2}{6.8}+...+\frac{1}{2}.\frac{2}{\left(2n-2\right)2n}\)

\(=\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{\left(2n-2\right)2n}\right)\)

\(=\frac{1}{2}\left(\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{2n-\left(2n-2\right)}{\left(2n-2\right)2n}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2n-2}-\frac{1}{2n}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2n}\right)=\frac{1}{4}-\frac{1}{4n}\)

kết quả hơi sai sai ak nha

\(A=2+2^2+2^3+...+2^{60}\)

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)

\(A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\)

\(A=2.3+2^3.3+...+2^{59}.3\)

\(A=3\left(2+2^3+...+2^{59}\right)\)

 Vì \(3\left(2+2^3+...+2^{59}\right)⋮3\)

\(\Rightarrow A⋮3\)

\(A=2+2^2+2^3+...+2^{60}\)

\(A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)

\(A=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{58}\left(1+2+2^2\right)\)

\(A=2.7+2^4.7+...+2^{58}.7\)

\(A=7\left(2+2^4+...+2^{58}\right)\)

Vì \(7\left(2+2^4+...+2^{58}\right)⋮7\)

\(\Rightarrow A⋮7\)

Ta có 

38=19.2

40=2³.5

ƯCLN(38,40)=2

ƯC(38,40)=Ư(2)={1;2}

vậy ƯC(38,40)={1;2}

Ta có : 

\(n+6⋮n+1\)

\(n+1⋮n+1\)

\(\Rightarrow\left(n+6\right)-\left(n+1\right)⋮n+1\)

\(n+6-n-1⋮n+1\)

\(5⋮n+1\)

\(\Rightarrow n+1\in\text{Ư}\left(5\right)\)

\(\Rightarrow n+1\in\left\{1;-1;5;-5\right\}\)

\(\Rightarrow n\in\left\{0;-2;4;-6\right\}\)

x = 2 

5²⁺¹  +  5²⁺²  = 750