`36-48:(x-3)=12`

`=>48:(x-3)=36-12=24`

`=>x-3=48:24=2`

`=>x=2+3=5`

Vậy : `x=5`

\(N=1.4+2.5+3.6+...+199.202\\ =1.\left(1+3\right)+2\left(2+3\right)+3\left(3+3\right)+...+199.\left(199+3\right)\\ =1\left(1+1+2\right)+2\left(2+1+2\right)+3\left(3+1+2\right)+...+199\left(199+1+2\right)\\ =1.2+2.3+3.4+...+199.200+2\left(1+2+3+...+199\right)\\ =\dfrac{199.\left(199+1\right)\left(199+2\right)}{3}+2\left(\dfrac{1+199}{2}.199\right)\\ =\dfrac{199.200.201}{3}+200.199\\ =199.200.67+199.200\\ =68.199.200\)

`A=2+2^2+2^3+...+2^{12}`

`=(2+2^2)+(2^3+2^4)+...+(2^{11}+2^{12})`

`=2.(1+2)+2^{3}.(1+2)+...+2^{11}.(1+2)`

`=2.3+2^{3}.3+...+2^{11}.3`

`=3(2+2^{3}+...+2^{11})\vdots 3`

\(a=2+2^2+2^3+...+2^{12}\\ \Rightarrow2a=2^2+2^3+2^4+...+2^{13}\)

\(\Rightarrow a=2a-a=2^{13}-2=2\left(2^{12}-1\right)\\ =2\left(2^6-1\right)\left(2^6+1\right)=2.63.62\)

Vì 63 ⋮ 3 ⇒  a⋮ 3

Bạn xem lại đề -.-"

Ta có :

B = 1 + 5 + 5² + 5³ + ... + 5¹⁰⁰

=> 5B = 5 + 5² + 5³ + 5⁴ + ... + 5¹⁰¹

=> 5B-B = (5+5²+5³+...+5¹⁰¹)-(1+5+5²+...+5¹⁰⁰)

=> 4B = 5¹⁰¹-1

=> B = \(\dfrac{5^{101}-1}{4}\)

a) 42 . 12 = 42 ( 10 + 2 ) = 42 . 10 + 42 . 2 = 420 + 84 = 504

a ( b + c ) = a . b + a .c 

b) 25 . 996 = 25 ( 1000 - 4 ) = 25 . 1000 - 25 . 4 = 25000 - 100 = 24900

a ( b - c ) = a . b - a . c

Nếu a=2 => b=0(vì nếu b>2 thì >2022)=>cd+c+d=20 => c<2(vì nếu c=2 thì >20) => c=1(vì nếu c=0=>d=10)=>2d=9(vô lí)

=>a=1 => b=9(vì nếu b<9 thì <1927) => cd+c+d=112 => c=9(vì nếu c<9 thì <107) => 2d=13( vô lí)

Vậy không tìm dc a, b, c, d

Sai đề rồi nha e

Khi x=2 thì không chia hết cho 3

n+5 ⋮ n+1

=> (n+1)+4 ⋮ n+1

=> 4 ⋮ n+1

=> n+1 ∈ Ư(4) = { 1;2;4}

=> n ∈ { 0;1;3 }

n+5 ⋮ n+1

\(\Rightarrow\) (n+1)+4 ⋮ n+1

\(\Rightarrow\) 4 ⋮ n+1

\(\Rightarrow\) n+1 ∈ Ư(4) = \(\left\{1,2,4\right\}\)

\(\Rightarrow\) n ∈  \(\left\{0,1,3\right\}\)

1050 số nhé