Lời giải:

$M=(\frac{2}{3})^2+(\frac{2}{3})^4+(\frac{2}{3})^6+...+(\frac{2}{3})^{100}$

$M.(\frac{2}{3})^2=(\frac{2}{3})^4+(\frac{2}{3})^6+(\frac{2}{3})^8+...+(\frac{2}{3})^{102}$

$\Rightarrow M-M(\frac{2}{3})^2=(\frac{2}{3})^2-(\frac{2}{3})^{102}$

$\Rightarrow M.\frac{5}{9}=(\frac{2}{3})^2-(\frac{2}{3})^{102}$

$\Rightarrow M=\frac{9}{5}\left[(\frac{2}{3})^2-(\frac{2}{3})^{102}\right]$

b.

Theo kết quả phần a:

$M.\frac{5}{9}=(\frac{2}{3})^2-(\frac{2}{3})^{102}=(\frac{2}{3})^2-(\frac{2}{3})^{3(x+7)}$

$\Rightarrow 102=3(x+7)$

$\Rightarrow x+7=34$

$\Rightarrow x=27$

Câu 1:

a. Gọi $d=ƯCLN(2n+3, 4n+4)$

$\Rightarrow 2n+3\vdots d; 4n+4\vdots d$

$\Rightarrow 2(2n+3)-(4n+4)\vdots d$

$\Rightarrow 2\vdots d\Rightarrow d\in \left\{1;2\right\}$

Mà $2n+3\vdots d$ nên $d$ lẻ. Do đó $d=1$

Vậy $ƯCLN(2n+3, 4n+4)=1$ nên phân số trên tối giản.

b. 

Gọi $d=ƯCLN(21n+4, 14n+3)$

$\Rightarrow 21n+4\vdots d; 14n+3\vdots d$

$\Rightarrow 3(14n+3)-2(21n+4)\vdots d$

$\Rightarrow 1\vdots d\Rightarrow d=1$

Vậy $ƯCLN(21n+4, 14n+3)=1$ nên phân số trên tối giản.

Câu 2:

a. Gọi $d=ƯCLN(3n+2, 7n+1)$

$\Rightarrow 3n+2\vdots d; 7n+1\vdots d$

$\Rightarrow 7(3n+2)-3(7n+1)\vdots d$

$\Rightarrow 11\vdots d$

Để phân số đã cho tối giản thì $3n+2\not\vdots 11$
$\Rightarrow 3n+2-11\not\vdots 11$

$\Rightarrow 3n-9\not\vdots 11$

$\Rightarrow 3(n-3)\not\vdots 11\Rightarrow n-3\not\vdots 11$

$\Rightarrow n\neq 11k+3$ với $k$ là số tự nhiên bất kỳ.

b.

Gọi $d=ƯCLN(2n+7, 5n+2)$

$\Rightarrow 2n+7\vdots d; 5n+2\vdots d$

$\Rightarrow 5(2n+7)-2(5n+2)\vdots d$

$\Rightarrow 31\vdots d$

Để phân số đã cho tối giản thì $2n+7\not\vdots 31$

$\Rightarrow 2n+7-31\not\vdots 31$

$\Rightarrow 2n-24\not\vdots 31$

$\Rightarrow 2(n-12)\not\vdots 31$
$\Rightarrow n-12\not\vdots 31$

$\Rightarrow n\neq 31k+12$ với $k$ là số tự nhiên bất kỳ.

câu văn miêu tả biển là "Cát càng mịn, biển càng trong" bạn nhé

1. Does your room have a colorful picture
2. Nobody in his class is better at English than Peter
3. Why don't we have a picnic in the park on the weekend
4. My house is not far from the supermarket
5. What is the price of these red notebooks
6. Many people go to work by walking for their health
7, How many hours do you spend watching television
8. Shall we go to the cinema tonight
9. The novel was much more interesting than the film
10. He seemed like a friendly person, but I didn't like him

1. Is there a colorful picture in your room ?

   Does ………your room have a colorful picture……………………………………………………………….?

2. Peter is best at English in his class.

   Nobody …in Peter's class is as good at English as him………………………………………………………………?

3. Let’s have a picnic in the park on the weekend.

   Why …don't we have a picnic in the park on the weekend……………………………………………………………………..?

4. My house is near the supermarket .

   My house is not ……far from the supermerket……………………………………………………?

5. How much are these red notebooks .

   What ……is the price of these red notebooks…………………………………………………………………..?

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tại vì mình nhấn mãi ko đc nên mình nhấn đại

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