\(A=\left(1+7\right)+...+7^{2020}\left(1+7\right)=8\left(1+...+7^{2020}\right)⋮8\)

\(A = (1 + 7) +...+7^2\)\(^0\)\(^2\)\(^0\) \((1 + 7) = 8 (1+...+7^2\)\(^0\)\(^2\)\(^0\)\() \) ⋮\(8\)

b) Để 4x + 19 chia hết cho x + 1 thì 15 chia hết cho x + 1

--> x + 1 là ước của 15

TH1: x + 1 = 15 <=> x = 14

TH2: x + 1 = 1 <=> x = 0

TH3: x + 1 = 3 <=> x = 2

TH4: x + 1 = 5 <=> x= 4

\(7^1+7^2+7^3+...+7^{117}+7^{118}=7\left(1+7+7^2\right)+7^4\left(1+7+7^2\right)+...+7^{116}\left(1+7+7^2\right)\)

\(=7.57+7^4.57+...+7^{116}.57=57\left(7+7^4+...+7^{116}\right)⋮57\)

Đặt B=71⁹+71⁸+71⁷+...+71²+71

 71B=71¹⁰+71⁹+71⁸⁺71⁷+...+71²

71B-B=71¹⁰-71

70B=71¹⁰-71=>B=\(\frac{71^{10}-71}{70}\)

Ta có A=70.\(\frac{71^{10}-71}{70}\)

            =71¹⁰-71

vậy còn 70

Cái chỗ ta có A=... tớ nhân với 70 rồi còngif

Đặt \(A=70\cdot\left(71^9+71^8+...+71^2+71+1\right)+1\)

Đặt \(B=71^9+71^8+...+71^2+71^1+71^0\)

\(\Leftrightarrow71B=71^{10}+71^9+...+71^3+71^2+71\)

\(\Leftrightarrow B=\dfrac{71^9-1}{70}\)

\(A=70\cdot B+1=71^9-1+1=71^9\)

Đặt \(A=71^9+71^8+...+71^2+71+1\)

\(\Rightarrow71A=71^{10}+71^9+...+71^2+71\)

\(\Leftrightarrow70A=71^9-1\)

hay \(A=\dfrac{71^9-1}{70}\)

\(C=70\cdot A+1\)

\(=71^9-1+1=71^9\)

70. Everybody is here now, ___aren't they_______?

71. There is nothing wrong, _____isn't there_____?

72. Mike mustn’t come late, ____must he______?

73. She is collecting stamps, ____isn't she______?

74. They often watch TV in the afternoon, ______don't they____?

75. David has cleaned your bike, ____hasn't he______?

76. John and Max don't like Maths, ____do they______?

77. Peter played handball yesterday, ______didn't he____?

78. Mary didn't do her homework last Monday, ____did she______?

79. Lewis could have bought a new car, ______couldn't he____?

80. The train is arriving on time, ____isn't it______?

81. Kevin spent all his money yesterday, ____didn't he______?

82. He had hardly left the office when the telephone rang, _____hadn't he_____?

83. Max'd better stay here for a week, ____shouldn't he______?

84. Nothing was damaged during the storm, ______was it____?

85. Mrs. Black doesn't believe her son is able to draw such a picture, _____does she_____?

86. He comes late sometimes, ____doesn't he______?

87. He failed to do anything last weekend, ____didn't he______?

88. The Smiths hardly ever go on travel, __does they______?

89. Jack and Jill went up the hill, ____don't they______?

90. There are seven days in a week, ________aren't there__? 

Giải:

a)    A = 21 + 22 + 23 + 24 + .............. + 22010

Ta có :

Trong 1 tích chỉ cần có 1 số chia hết cho n thì tích đó chia hết cho n mà 21 \(⋮\)cả 3 và 7

=>  A \(⋮\)cả 3 và 7

Vây  A \(⋮\)cả 3 và 7

b) B = 31 + 32 + 33 + 34 + ............... + 22010

Ta có :

Trong 1 tích chỉ cần có 1 số chia hết cho n thì tích đó chia hết cho n 

mà 32 \(⋮\)4

Vì dãy số trên là các số tự nhiên có khoảng cách là 1 nên 39 nằm trong dãy số đó mà 39 \(⋮\)13

=> B \(⋮\)cả 4 và 13

Vậy  B \(⋮\)cả 4 và 13

c)  C = 51 + 52 + 53 + 54 + ................... + 52010

Ta có : 

Trong 1 tích chỉ cần có 1 số chia hết cho n thì tích đó chia hết cho n

mà 54 \(⋮\)6

Vì dãy số trên là các số tự nhiên có khoảng cách là 1 nên 62 nằm trong dãy số đó mà 62 \(⋮\)31 

=> C \(⋮\)cả 6 và 31

Vậy C \(⋮\)cả 6 và 31

d)  D = 71 + 72 + 73 + 74 + ...................... + 72010

Ta có :

Trong 1 tích chỉ cần có 1 số chia hết cho n thì tích đó chia hết cho n

mà 72 \(⋮\)8

Vì dãy số trên là các số tự nhiên có khoảng cách là 1 nên 114 nằm trong dãy số đó mà 114 \(⋮\)57

=> D \(⋮\)cả 8 và 57

Vậy  D \(⋮\)cả 8 và 57

Học tốt!!!

70.They sell jeans all over the world. →Jeans………………ARE SOLD ALL OVER THE WORLD…………………………………………
71. They have found oild in the Antarctic →Oil………………HAS BEEN FOUND IN THE ANTARCTIC………………………………………………
72. They will probably translate her new book into English.
→Her new book………………WILL PROBABLY BE TRANSLATED INTO ENGLISH…………………………………..
73. Someone gave her this book an hour ago. →She……………………WAS GIVEN THIS BOOK AN HOUR AGO………………………………………..
74. Has someone repaired this telephone? →Has…………………THIS TELEPHONE BEEN REPAIRED?……………………………………….
75. “What do you think of the canteen coffee?” ask Ann. →Ann………………………………ASKED WHAT I THOUGHT OF THE CANTEEN COFFEE………………………………
76. “What foreign languages do they teach besides English?”
→I asked……………………WHAT FOREIGN LANGUAGES THEY TAUGHT BESIDES ENGLISH…………………………………
77. He has never played a computer game before.
→This is the first…………HE HAS EVER PLAYED  COMPUTER GAME ………………………………………
78. “Please lend me your dictionary, Quang,” said Hoa. →Hoa…………………………TOLD QUANG TO LEND HẺ HIS DICTIONARY………………………………….
79. “Can you turn down the radio?” Miss Jackson said to Mary.
→Miss Jackson……………ASKED MARY TO TURN DOWN THE RADIO……………………………………..
80. I last wrote to my uncle in July.
→I haven’t………………………WRITTEN TO MY UNCLE SINCE JULY………………………………..

70.They sell jeans all over the world. →Jeans are sold over the world.
71. They have found oild in the Antarctic →Oil has been found in the Antarctic.
72. They will probably translate her new book into English.
→Her new book will be probably translated into English.
73. Someone gave her this book an hour ago. →She was given this book an hour ago
74. Has someone repaired this telephone? →Has this telephone been repaired?
75. “What do you think of the canteen coffee?” ask Ann. →Ann ask me what I thought of the canteen coffee
76. “What foreign languages do they teach besides English?”
→I asked what foreign languages they taught besides English
77. He has never played a computer game before.
→This is the first time he has played a computer game.
78. “Please lend me your dictionary, Quang,” said Hoa. →Hoa told Quang to lend her his dictionary
79. “Can you turn down the radio?” Miss Jackson said to Mary.
→Miss Jackson told Mary to turn down the radio
80. I last wrote to my uncle in July.
→I haven’t written to my uncle in July

70.They sell jeans all over the world. →Jeans…are sold all over the world………………………………………………………
71. They have found oild in the Antarctic →Oil……has been found in the Antartica…………………………………………………………
72. They will probably translate her new book into English.
→Her new book…will probably be translated into English………………………………………………..
73. Someone gave her this book an hour ago. →She……was given this book an hour ago………………………………………………………..
74. Has someone repaired this telephone? →Has………this telephone been repaired?………………………………………………….
75. “What do you think of the canteen coffee?” asked Ann. →Ann…asked me if I thought of the canteen coffee……………………………………………………………
76. “What foreign languages do they teach besides English?”
→I asked…what foreign languages they taught besides English……………………………………………………
77. He has never played a computer game before.
→This is the first…time he has played a computer game………………………………………………
78. “Please lend me your dictionary, Quang,” said Hoa. →Hoa…told me to lend her my dictionary………………………………………………………….
79. “Can you turn down the radio?” Miss Jackson said to Mary.
→Miss Jackson…told Mary to turn down the radio ………………………………………………..
80. I last wrote to my uncle in July.
→I haven’t…written to my uncle since July……………………………………………………..