`#3107.101107`

`A = 1+ 3 + 3^2+3^3+…+3^101?`

`= (1 + 3 + 3^2) + (3^3 + 3^4 + 3^5) + ... + (3^99 + 3^100 + 3^101)`

`= (1 + 3 + 3^2) + 3^3 * (1 + 3 + 3^2) + ... + 3^99 * (1 + 3 + 3^2)`

`= (1 + 3 + 3^2) * (1 + 3^3 + ... + 3^99)`

`= 13 * (1 + 3^3 + ... + 3^99)`

Vì `13 * (1 + 3^3 + ... + 3^99) \vdots 13`

`=> A \vdots 13`

Vậy, `A \vdots 13.`

Yêu cầu là gì ạ?

\(B=3+3^2+3^3+...+3^{300}\)

\(B=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{298}+3^{299}+3^{300}\right)\)

\(B=\left(3+3^2+3^3\right)+3^3\cdot\left(3+3^2+3^3\right)+...+3^{297}\cdot\left(3+3^2+3^3\right)\)

\(B=39+3^3\cdot39+...+3^{297}\cdot39\)

\(B=39\cdot\left(1+3^3+...+3^{297}\right)\)

Vậy B chia hết cho 39

Các số hạng trong tổng \(A\) đều chia hết cho \(3\) nên \(\Rightarrow A⋮3\)

Vậy \(A⋮3\)

A=3+3^2+3^3+3^4+...+3^12

A=(3+3^2+3^3)+(3^4+3^5+3^6)+.....+(3^10+3^11+3^12)   (gộp nhóm)

A=3.(1+3+3^2)+3^4.(1+3+3^2)+......+3^10.(1+3+3^2)        (phân phối)

A=3.13+3^4.13+....+3^10.13

A=13.(3+3^4+....+3^10)

Vì 13⋮13

nên 13.(3+3^4+...+3^10)⋮13

=>A⋮13

chia hết cho 13 hay 3 vậy bạn?(mink thấy sai sai)

mk viết lại đề nha

\(7\times5^2-32\div2^3+3^2\)

\(7\times25-2^5\div2^3+9\)

\(175-2^2+9\)

\(175-4+9\)

\(180\)

tk mk nha bn____________!!

7 x 25 - 2⁵ : 2³ + 9

175 - 2² + 9

175 - 4 + 9

= 180

Đáp án đúng là : 180

tk to nha

7 x 5 ^ 2 - 32 : 2 ^ 3 + 3 ^ 2

= 7 x 25 - 2⁵ : 2³ + 9

= 175 - 4² + 9

= 175 - 4 + 9

= 180

36.

\(Q=x-2+\dfrac{3}{x-2}+2\ge2\sqrt{\dfrac{3\left(x-2\right)}{x-2}}+2=2\left(\sqrt{3}+1\right)\)

39.

\(\dfrac{\sqrt{3}cosx+sinx}{2cosx+3sinx}=\dfrac{\dfrac{\sqrt{3}cosx}{sinx}+\dfrac{sinx}{sinx}}{\dfrac{2cosx}{sinx}+\dfrac{3sinx}{sinx}}=\dfrac{\sqrt{3}cotx+1}{2cotx+3}=\dfrac{\sqrt{3}.\left(-\dfrac{1}{2}\right)+1}{2.\left(-\dfrac{1}{2}\right)+3}=\dfrac{2-\sqrt{3}}{4}\)

\(\Rightarrow\left\{{}\begin{matrix}a=2\\b=1\end{matrix}\right.\) \(\Rightarrow a-4b=-2\)

40. \(\overrightarrow{BA}=\left(6;4\right)=2\left(3;2\right)\Rightarrow\) trung trực AB nhận (3;2) là 1 vtpt

Gọi M là trung điểm AB \(\Rightarrow M\left(-1;3\right)\)

Phương trình trung trực AB:

\(3\left(x+1\right)+2\left(y-3\right)=0\Leftrightarrow3x+2y-3=0\)

S = 1 + 3 + 3² + 3³ + ... + 3⁵⁹

S = ( 1 + 3 + 3² ) + ( 3³ + 3⁴ + 3⁵ ) + ... + ( 3⁵⁷ + 3⁵⁸ + 3⁵⁹ )

S = 13 + 3³( 1 + 3 + 3² ) + ... + 3⁵⁷( 1 + 3 + 3² )

S = 13 + 3³ . 13 + ... + 3⁵⁷ . 13

S = 13 ( 1 + 3³ + ... + 3⁵⁷ ) ⋮ 13 vì 13 ⋮ 13

Vậy S ⋮ 13

\(S=1.\left(1+3\right)+3^2\left(1+3\right)+3^4\left(1+3\right)+...+3^8\left(1+3\right)\)

\(S=4x\left(1+3^2+...+3^8\right)\)

Vì 4 chia hết cho 4 nên S chia hết cho 4

33. He didn't know where to find more information about that.

34. The teacher says that I'm the noisiest student in the school.

35. The city hasn't changed since the 1990s.

36. He is used to drinking coffee in the morning.

29, independence

30,inventors

31,Disneyland has attracted over 670 million people since it opened in 1955

32,The house reicive energy of the sun from the solar panels are installed on the roof

33,He didn't know where he can find more information about that

34,The teacher says that I'm the noisiest student in the school

35,The city hasn't changed since it was in 1990s

36,He is used to drinking coffe in the morning