Question2: Rearrange the following words and phrased to make complete sentences.

most/ is/ house/ which/ for/ the/ and/ family/ suitable/ Mr.Nam/ his/ ?/
=> Which is the most suitable house for Mr.Nam and his family?

are/ in/ the/ playing/ the/ schoolyard/ corner/ marbles/ of/ boys/ a/ of/ some/.
=> Some of the boys are playing marbles in a corner of the schoolyard.

like/ walk/ a/ would/ have/ you/ show/ after/ musical/ the/ to/?/.
=> Would you to have a walk after the musical show ?

summer/ in/ students/ going/ the/ in/ school/ are/ my/ forty/ visit/ to/ citadel/ this/ Hue/ .
=> Forty students in my school are going to visit the citadel in Hue this summer

is/ one/ the/ after-school/ populer/ most/ USA/ of/ baseball/ the/ in/ activities
baseball is one of the most popular activities after school in the USSA

Còn Question1 đâu bạn?

4/9

giải các bước ra giúp mình

1. that is an intelligent dog

2. i took the bus to school

3. how many plums do you want to buy ?

4. i find collecting old comic bbooks interesting

câu a)

\(S=3^0+3^2+3^4+...+3^{2002}\\ \Rightarrow9S=3^2+3^4+3^6+...+3^{2004}\)

từ đó ta suy ra : \(9S-S=\left(3^2+3^4+...+3^{2004}\right)-\left(3^0+3^2+3^4+...+3^{2002}\right)\)

vậy \(8S=3^{2004}-1\Rightarrow S=\dfrac{3^{2004}-1}{8}\)

b) các số mũ lần lượt như sau : \(0;2;4;6;8;...;2002\)

ta có các dãy số hạng của những số trên là :

\(\left(2002-0\right)\div2+1=1002\) (số)

số nhóm mà chúng ta có thể ghép được là :

\(\dfrac{1002}{3}=334\) \(\left(nhóm\right)\)

\(\Rightarrow S=\left(3^0+3^2+3^4\right)+\left(3^6+3^8+3^{10}\right)+...+\left(3^{1998}+3^{2000}+3^{2002}\right)\\ \Rightarrow S=\left(3^0+3^2+3^4\right)+3^6\times\left(3^0+3^2+3^4\right)+...+3^{1998}\times\left(3^0+3^2+3^4\right)\\ \Rightarrow S=1\times91+3^6\times91+...+3^{1998}\times91=\left(1+3^6+...+3^{1998}\right)\times91\)TA CÓ 91 CHIA HẾT CHO 7 CHO NÊN TA KẾT LUẬN RẰNG S ⋮ 7

         S = 3⁰ + 3² + 3⁴ +.....+ 3²⁰⁰²

      3²S =         3²  + 3⁴+.....+3²⁰⁰² + 3²⁰⁰⁴

9S -  S  = 3²⁰⁰⁴ - 1

       8S =  3²⁰⁰⁴ - 1

         S = (3²⁰⁰⁴ - 1)/8

S = 3⁰ + 3² + 3⁴ +....+3²⁰⁰²

Xét dãy số : 0; 2; 4; ....;2002

Dãy số trên có số hạng là : (2002 - 0) : 2 + 1  = 1002 ⋮ 2

Nhóm 2 số hạng liên tiếp của tổng S thành 1 nhóm ta được

S = (3⁰ + 3²) +( 3² + 3⁴) +....+ ( 3²⁰⁰⁰+3²⁰⁰²)

S = 28 + 3².( 1+3²) +....+ 3²⁰⁰⁰.( 1+3²)

S = 28 + 3². 28 +....+ 3²⁰⁰⁰.28

S = 28 .( 1 + 3²+....+3²⁰⁰⁰) 

vì 28 ⋮ 7 ⇒ 28.( 1 + 3² +.....+ 3²⁰⁰⁰) ⋮ 7

⇒ A = 3⁰ + 3² + 3⁴ +....+3²⁰⁰² ⋮ 7 (đpcm)

\(3A=3+3^2+3^3+..+3^{3001}\)

\(3A-A=\left(3+3^2+3^3+...+3^{3001}\right)-\left(1+3^2+3^3+..+3^{3000}\right)\)

\(2A=3^{3001}-1\)

\(A=\dfrac{3^{3001}-1}{2}=\dfrac{3^{3001}}{2}-\dfrac{1}{2}\)

`G=1-5+5^{2}-5^{3}+5^{4}-...-5^{199}-5^{200}`

`5G=5-5^{2}+5^{3}-5^{4}+5^{5}-...-5^{200}-5^{201}`

`=>5G+G=1-2.5^{200}-5^{201}`

\(=>G=\dfrac{1-2.5^{200}-5^{201}}{6}\)

`D=1+4-4^{2}+4^{3}-4^{4}+...+4^{99}-4^{100}`

`4D=4+4^{2}-4^{3}+4^{4}-4^{5}+....+4^{100}-4^{101}`

`=>4D+D=1+4+4-4^{101}`

=>5D=9-4^{101}`

\(=>D=\dfrac{9-4^{101}}{5}\)