Cminh: (70+71+72+73+...+72008+72009) chia het cho 8
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NT
2
10 tháng 1 2022
\(A=\left(1+7\right)+...+7^{2020}\left(1+7\right)=8\left(1+...+7^{2020}\right)⋮8\)
10 tháng 1 2022
\(A = (1 + 7) +...+7^2\)\(^0\)\(^2\)\(^0\) \((1 + 7) = 8 (1+...+7^2\)\(^0\)\(^2\)\(^0\)\() \) ⋮\(8\)
8 tháng 11 2021
\(7^1+7^2+7^3+...+7^{117}+7^{118}=7\left(1+7+7^2\right)+7^4\left(1+7+7^2\right)+...+7^{116}\left(1+7+7^2\right)\)
\(=7.57+7^4.57+...+7^{116}.57=57\left(7+7^4+...+7^{116}\right)⋮57\)
AT
3
2 tháng 4 2020
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
22 tháng 6 2022
Đặt \(A=70\cdot\left(71^9+71^8+...+71^2+71+1\right)+1\)
Đặt \(B=71^9+71^8+...+71^2+71^1+71^0\)
\(\Leftrightarrow71B=71^{10}+71^9+...+71^3+71^2+71\)
\(\Leftrightarrow B=\dfrac{71^9-1}{70}\)
\(A=70\cdot B+1=71^9-1+1=71^9\)
PD
1
16 tháng 5 2022
Đặt \(A=71^9+71^8+...+71^2+71+1\)
\(\Rightarrow71A=71^{10}+71^9+...+71^2+71\)
\(\Leftrightarrow70A=71^9-1\)
hay \(A=\dfrac{71^9-1}{70}\)
\(C=70\cdot A+1\)
\(=71^9-1+1=71^9\)
KY
14 tháng 7 2021
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__?
DN
5 tháng 11 2020
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!!!
KY
20 tháng 2 2022
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………………………………..
PP
20 tháng 2 2022
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
Ta co
(70+71+72+73+...+72008+72009)
=(1 + 7) + (72 + 73) +.... +(72008 + 72009)
=8 + 72.8 + .... +72008.8
=8.(1 + 72 + .... + 72008) chia het cho 8
Ta co
(70+71+72+73+...+72008+72009)
=(1 + 7) + (72 + 73) +.... +(72008 + 72009)
=8 + 72.8 + .... +72008.8
=8.(1 + 72 + .... + 72008) chia het cho 8