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![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(A=2\left(1+2+2^2\right)+...+2^{19}\left(1+2+2^2\right)\)
\(=7\left(2+...+2^{19}\right)⋮7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(A=2\left(1+2+2^2\right)+...+2^{19}\left(1+2+2^2\right)\)
\(=7\left(2+...+2^{19}\right)⋮7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(A=2\left(1+2+2^2\right)+...+2^{19}\left(1+2+2^2\right)\)
\(=7\cdot\left(2+...+2^{19}\right)⋮7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2+2^2+2^3+2^4+...+2^{100}\)
\(=2+\left(2^2+2^3+2^4\right)+...+\left(2^{98}+2^{99}+2^{100}\right)\)
\(=2+2^2\left(1+2+2^2\right)+...+2^{98}\left(1+2+2^2\right)\)
\(=2+7\cdot\left(2^2+2^5+...+2^{98}\right)\)
=>A không chia hết cho 7 mà là chia 7 dư 2 nha bạn
![](https://rs.olm.vn/images/avt/0.png?1311)
a. Ta có : A = \(5+5^2+5^3+...+5^{100}\) = \(\left(5+5^2\right)+\left(5^3+5^4\right)+...\left(5^{99}+5^{100}\right)\)
= \(5\left(1+5\right)+5^3\left(1+5\right)+...+5^{99}\left(1+5\right)\)= \(6\left(5+5^3+5^4+...+5^{99}\right)\)
= \(6.5\left(1+5+5^2+...+5^{98}\right)\)= \(30\left(1+5+5^2+...+5^{98}\right)\)
Vậy A = \(30\left(1+5+5^2+...+5^{98}\right)\)
b. Vì A = \(30\left(1+5+5^2+...+5^{98}\right)\)nên A chia hết cho 30
Không biết đúng hay không
Sai thì thôi nhé !
![](https://rs.olm.vn/images/avt/0.png?1311)
b: \(B=\left(1+7\right)+7^2\left(1+7\right)+...+7^{100}\left(1+7\right)\)
\(=8\cdot\left(1+7^2+...+7^{100}\right)⋮8\)
c: \(C=4^{39}\left(1+4+4^2\right)=4^{39}\cdot21=4^{38}\cdot84⋮28\)
`A=2+2^2+2^3+...+2^{12}`
`=(2+2^2)+(2^3+2^4)+...+(2^{11}+2^{12})`
`=2.(1+2)+2^{3}.(1+2)+...+2^{11}.(1+2)`
`=2.3+2^{3}.3+...+2^{11}.3`
`=3(2+2^{3}+...+2^{11})\vdots 3`
\(a=2+2^2+2^3+...+2^{12}\\ \Rightarrow2a=2^2+2^3+2^4+...+2^{13}\)
\(\Rightarrow a=2a-a=2^{13}-2=2\left(2^{12}-1\right)\\ =2\left(2^6-1\right)\left(2^6+1\right)=2.63.62\)
Vì 63 ⋮ 3 ⇒ a⋮ 3