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*Sửa lại đề*
A = 21+ 22+ 23+ 24 + .. + 2100
A = (21+22) + (23+ 24) +...+ (299+ 2100)
A = 2.(1+2) + 23.(1+2) + .. + 299. (1+2)
A = 2.3 + 23. 3 + .. + 299.3
A = 3 . (21 + 23 + .... + 299)
Mà 3 chia hết cho 3
=> A chia hết cho 3
![](https://rs.olm.vn/images/avt/0.png?1311)
2A - A= 221chia hết cho 27
suy ra A chia hết cho 128
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A=1+2+2^2+2^3+...+2^{99}\)
\(\Rightarrow2A=2+2^2+2^3+...+2^{100}\)
\(\Rightarrow A=2A-A=2+2^2+...+2^{100}-1-2-2^2-...-2^{99}=2^{100}-1\)
b) \(A=1+2+2^2+...+2^{99}=\left(1+2+2^2+2^3\right)+2^4\left(1+2+2^2+2^3\right)+...+2^{96}\left(1+2+2^2+2^3\right)\)
\(=15+2^4.15+...+2^{96}.15=15\left(1+2^4+...+2^{96}\right)\)
\(=3.5\left(1+2^4+...2^{96}\right)\) chia hết cho 3 và 5
c) \(A=1+2+2^2+...+2^{99}\)
\(=1+2\left(1+2+2^2\right)+...+2^{97}\left(1+2+2^2\right)\)
\(=1+2.7+...+2^{97}.7=1+7\left(2+...+2^{97}\right)\) chia 7 dư 1
=> A không chia hết cho 7
![](https://rs.olm.vn/images/avt/0.png?1311)
A=2(1+2)+2^3(1+2)+...+2^2009(1+2)
=3(2+2^3+...+2^2009) chia hết cho 3
A=2(1+2+2^2)+2^4(1+2+2^2)+...+2^2008(1+2+2^2)
=7(2+2^4+...+2^2008) chia hết cho 7
![](https://rs.olm.vn/images/avt/0.png?1311)
A = \(4+4^2+4^3+.....+4^{23}+4^{24}\)
= \(4\left(1+4+4^2\right)+.....+4^{22}+\left(1+4+4^2\right)\)
= \(4.21+.....+4^{22}.21\)
= \(21\left(4+...+4^{22}\right)⋮21\)
Vậy A chia hết cho 21
Ai k mik mik k lại nha
Lâu r chị k nhớ lắm nhé
CM A chia hết cho 20
A = 4(1+4+4^2+...+4^23) chia hết cho 4 (1)
A = (4+4^2) + (4^3+4^4) + ...+ (4^23+4^24)
= 4(1+4) + 4^3(1+4) +...+4^23(1+4)
= (1+4)(4+4^3+4^5+...+4^23)
=5.(4+4^3+4^5+...+4^23) chia hết cho 5 (2)
Mà UCLN(4,5)=1 (3)
Vậy A chia hết cho 4.5 =20
CM A chia hết cho 21
A = (4+4^2+4^3)+(4^4+4^5+4^6)+...+(4^22+4^23+4^24)
= 4(1+4+4^2) +4^4(1+4+4^2)+...+4^22(1+4+4^2)
= (1+4+4^2)(4+4^4+...+4^22)
= 21(4+4^4+...+4^22) chia hết cho 21
Vậy A chia hết cho 24.
Chúc e học giỏi!
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=4+2^2+2^3+...+2^{20}\)
\(\Rightarrow2A=8+2^3+2^4+...2^{21}\)
\(\Rightarrow2A-A=\left(8+2^3+2^4+...+2^{21}\right)-\left(4+2^2+2^3+...+2^{20}\right)\)
\(\Rightarrow A=8+2^{21}-4-2^2\)
\(\Rightarrow A=8+2^{21}-4-4\)
\(\Rightarrow A=2^{21}\)
Có: \(128=2^4\)
Mà \(2^{21}:2^7=2^{14}\)
\(\Rightarrow2^{21}⋮2^7\)
\(\Rightarrow A⋮2^7\)
\(\Rightarrow A⋮128\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=4+4+23+24+...+220 A=23+23+24+...+220 A=2.23+24+...+220 A=24+24+25+...+220 A=2.25+26+...+220 A=2.26+27+...+220 A=27(1+1+2+...+213)=128(1+1+2+...+213) chia hết cho 128
h nha
![](https://rs.olm.vn/images/avt/0.png?1311)
A=4+22 +23 +24 +....220
A=22+22 +23 +24 +....220
2A=2(4+22 +23 +24 +....220)
2A=23+23 +24 +25 +....221
2A-A=(23+23 +24 +25 +....221)-(22+22 +23 +24 +....220)
A=23+221-(22+22)
A=8+221-8
A=221
mà 221 chia hết cho 27
vậy A có chia hết cho 128
A chia hết cho128 nhé!