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\(A=2+2^2+2^3+...+2^{100}\)
\(\Rightarrow2A=2\left(2+2^2+2^3+...+2^{100}\right)\)
\(\Rightarrow2A=2^2+2^3+2^4+...+2^{101}\)
\(\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)\)
\(\Rightarrow A=2^{101}-2\)
\(\Rightarrow A-2=2^{101}-2-2=2^{101}-4\)
Ta có: \(A=2+2^2+2^3+...+2^{100}\)
\(2A=2^2+2^3+2^4+...+2^{101}\)
\(2A-A=2^{101}-2\)
Hay \(A=2^{101}-2\)
Vậy \(A=2^{101}-2\)
_Học tốt_
\(A=2+2^2+2^3+...+2^{99}+2^{100}\)
\(\Rightarrow2A=2^2+2^3+2^4+...+2^{100}+2^{101}\)
\(\Rightarrow A=2^{101}-2\)
\(\Rightarrow A+2=2^{101}-2+2\)
\(\Rightarrow A+2=2^{101}\)
\(A=2+2^2+2^3+...+2^{100}\)
\(\Rightarrow2A=2.\left(2+2^2+2^3+...+2^{100}\right)\)
\(\Rightarrow2A=2^2+2^3+2^4+...+2^{101}\)
\(\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)\)
\(\Rightarrow A=2^{101}-2\)
\(\Rightarrow A+1=2^{101}-2+2\)
\(\Rightarrow A+2=2^{101}\)
Vậy A+2=2101
Ta coi \(B=2^1+2^2+2^3+...+2^{100}\)
\(\Rightarrow A=B+2\)
Ta có:
\(B=2^1+2^2+2^3+...+2^{100}\)
\(\Rightarrow2B=\left(2^1+2^2+2^3+...+2^{100}\right).2\)
\(=2^2+2^3+2^4+...+2^{101}\)
\(\Rightarrow B=2B-B=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2^1+2^2+2^3+...+2^{100}\right)\)
\(=2^{101}-2\)
\(\Rightarrow A=2^{101}-2+2=2^{101}\)
A=1+2+22+23+...+2200
2A=2+22+23+24+...+2201
2A-A=(2+22+23+24+...+2201) - (1+2+22+23+...+2200)
A=2201-1
=>A+1=2201
B=3+32+33+...+32005
3B=32+33+34+...+32006
3B-B=(32+33+34+...+32006) - (3+32+33+...+32005)
2B=32006-3
2B+3=32006 là lũy thừa của 3 (đpcm)
A = 1 + 2 + 22 + 23 + ... + 2200
2A = 2 + 22 + 23 + 24 + ... + 2201
2A - A = ( 2 + 22 + 23 + 24 + ... + 2201 ) - ( 1 + 2 + 22 + 23 + ... + 2200 )
A = 2201 - 1
1) A = 1+2+2\(^2\) + ... + \(2^{200}\)
2A = 2 + 2\(^2\) + 2\(^3\) + ... + 2\(^{201}\)
2A - A = 2 + 2\(^2\) +2\(^3\) + ... + \(2^{201}\) - 1 - 2 - ... - 2\(^{200}\)
A = 2\(^{201}\) - 1
A+1 = 2\(^{201}\)
Vậy a + 1 = 2\(^{201}\)
2) C = 3 + 3\(^2\) + 3\(^3\) + ... + 3\(^{2005}\)
3C = 3\(^2\) + 3\(^3\) + 3\(^4\) + ... + 3\(^{2006}\)
3C - C = \(3^2\) + 3\(^3\) + 3\(^4\) + ... + 3\(^{2006}\) - 3 - 3\(^2\) - 3\(^3\) - ... - 3\(^{2005}\)
2C = 3\(^{2006}\) - 3
2C+3 = 3\(^{2006}\)
Vậy 2C + 3 là luỹ thừa của 3 ( Đpcm )
1.
A = 1 + 2 + 22 + 23 + ... + 2200
2A = 2 + 22 + 23 + 24 + ... + 2201
2A - A = (2 + 22 + 23 + 24 + ... + 2201) - (1 + 2 + 22 + 23 + ... + 2200)
A = 2201 - 1
=> A + 1 = 2201 - 1 + 1
=> A + 1 = 2201
2.
B = 3 + 32 + 33 + ... + 32005
3B = 32 + 33 + 34 + ... + 32006
3B - B = (32 + 33 + 34 + ... + 32006) - (3 + 32 + 33 + ... + 32005)
2B = 32006 - 3
=> 2B + 3 = 32006 - 3 + 3
=> 2B + 3 = 32006
Bài 2
A = 1 + 2 + 22 + 23 + ... + 2200
2A = 2 + 22 + 23 + 24 + ... + 2201
2A - A = (2 + 22 + 23 + 24 + ... + 2201) - (1 + 2 + 22 + 23 + ... + 2200)
A = 2201 - 1
=> A + 1 = 2201 - 1 + 1
=> A + 1 = 2201
Bài 3
B = 3 + 32 + 33 + ... + 32005
3B = 32 + 33 + 34 + ... + 32006
3B - B = (32 + 33 + 34 + ... + 32006) - (3 + 32 + 33 + ... + 32005)
2B = 32006 - 3
=> 2B + 3 = 32006 - 3 + 3
=> 2B + 3 = 32006
8=2^3 ; 20=20^1 ; 60=60^1 ; 90=90^1
16=2^4 ; 27=3^3 ; 81=3^4 ; 100=10^2
I. Find the word which has a different sound in the part underlined
1.
A.
come
B.
month
C.
mother
D.
open
2.
A.
hope
B.
homework
C.
one
D.
post
3.
A.
brother
B.
judo
C.
going
D.
rode
4.
A.
cities
B.
watches
C.
dishes
D.
houses
5.
A.
grandparents
B.
brothers
C.
uncles
D.
fathers
6.
A.
books
B.
walls
C.
rooms
D.
pillows
7.
A.
finger
B.
leg
C.
neck
D.
elbow
8.
A.
writes
B.
makes
C.
takes
D.
drives
9.
A.
request
B.
project
C.
neck
D.
exciting
10
A.
Thursday
B.
thanks
C.
these
D.
birthday
II. Find which word does not belong to each group.
1.
A.
toilet
B.
library
C.
kitchen
D.
bedroom
2.
A.
sofa
B.
dishwasher
C.
cupboard
D.
sink
3
A.
apartment
B.
villa
C.
silt house
D.
hotel
4.
A.
at
B.
apartment
C.
kitchen
D.
living room
5.
A.
television
B.
cook
C.
fridge
D.
cooker
III. Choose the best answer (A, B, C or D).
1. There are two lights ____ the ceiling.
A. in
B. at
C. on
D. between
2. There___ four chairs and a table _____the middle of the room.
A. are – in
B. are – at
C. is – on
D. is – in
3. They are moving ____a new apartment ____the city centre soon.
A. at – at
B. from – in
C. to – in
D. to – from
4. There are some dirty dishes_____ the floor.
A. on
B. with
C. in
D. for
5. My bedroom is _____the bathroom.
A. under
B. in
C. on
D. next to
6. There aren’t any pillows _____the bed.
A. in
B. on
C. behind
D. in front of
7. Can you ______ me the book, please?
A. move
B. pass
C. have
D. turn
8. Nga is _____ the phone, chatting ______friends.
A. on – to
B. on – on
C. to – with
D. to – to
9. My best friend is kind and _________ . He often makes me laugh.
A. funny
B. nice
C. shy
D. boring
10. The film is very _____ and we can’t see all of it.
A. wonderful
B. easy
C. exciting
D. boring
11. The summer camp is for students _________ between 10 and 15.
A. age
B. aged
C. aging
D. ages
12. Mary has __________ hair and big ___________eyes.
A. blonde, small
B. a black, blue
C. blonde, blue
D. black, long
13. Next summer I am working as a ___________ teacher in a village near Hoa Binh city.
A. volunteer
B. nice
C. good
D. favourite
14. She is always __________ at school and helps other students with their homework.
A. hard
B. hardly
C. hard-working
D. work hard
15. Our class is going to _______ a pinic at the zoo on Saturday. Would you to come with us?
A. have
B. take
C. pass
D. go
16. It’s ______ to go home. It’s so late.
A. now
B. sure
C. time
D.
17. Please turn ______ the lights. The room is so dark.
A. in
B. on
C. off
D. at
18. At break time, I go to the library and ______ books.
A. go
B. read
C. play
D. listen
19. Listen! Someone _________ at the door.
A. knock
B. knocks
C. is knocking
D. are knocking
20. Nam ___________ football now. He’s tired.
A. doesn’t play
B. plays
C. is playing
D. isn’t playing
21. We are excited ______ the first day of school.
A. at
B. with
C. about
D. in
22. My parents often help me __________ my homework.
A. at
B. with
C. about
D. in
23. I am having a math lesson but I forgot my _________. I have some difficulty.
A. calculator
B. bike
C. pencil case
D. pencil sharpener
24. In the afternoon, students ______ many interesting clubs.
A. join
B. do
C. play
D. read
25. School at 4.30 p.m every day.
A. finish
B. finishes
C. go
D. have
IV. Complete the sentences with the Present simple or the Present continuous form of the verbs.
1. They often (visit)________their parents in the holidays.
2. We (speak) French at the moment.
3. I (watch) _______TV about 3 hours a day.
4. My family usually (go)______to the movies on Sunday.
5. Look at the girl! She (ride)_________ a horse.
6. We (play)_________tennis now.
7. Minh sometimes (prace)_________the guitar in his room.
8.________you ()________ chocolate ice cream?
9. I really ()________ cooking.
10. Hung can’t answer the phone because he (take) ______________a shower.
V. Fill in each blank with a suitable verbs.
1. She _______an oval face
2. ______ Mai’s hair long or short? - It ________short.
3. He ________ tall and thin.
4. Toan ________ an athlete. He ____ very strong.
5. Ngan ______short black hair.
6. What color _______those bikes?
7. What color __________Nam’s eyes?
8. What _______those?
VI. Complete the passage with a suitable preposition.
We have English lessons (1)________Room 12. There are 24 tables for students and one desk for the teacher. (2)_________the walls, there are a lots of posters of England. There’s a cupboard at the front of the room and (3)________ the cupboard, there is a TV and DVD player. Sometimes we watch films. There are some bookshelves (4)______the classroom. (5)_______the shelves, there are a lot of English books. Our books are (6)________the teacher’s desk. He wants to look at our homework. Our school bags are (7)________the floor, and there is some food (8)________ the school bags. It’s now 5.30 pm. We are (9)_______home, but our teacher is (10)__________ school. He often stays late to prepare for tomorrow’s lessons.
VII. Reorder the words and write the meaning sentences.
1. city / beautiful / a / Ho Chi Minh /
..............................................................................................................
2.green fields / there /
..............................................................................................................
3. dog / it’s / friendly /
..............................................................................................................
4.student / Minh / new / a /
..............................................................................................................
5. television / big / a / there’s.
..............................................................................................................
6. new / four / there / cars /
..............................................................................................................
7. are / two / pizza / there /
..............................................................................................................
9.ten / are / desks / small /
..............................................................................................................
mình nhầm đó hihi
;)