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\(A=5+5^2+5^3+5^4+...+5^{11}+5^{12}\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{11}+5^{12}\right)\)
\(=\left(5+5^2\right)+5^2\left(5+5^2\right)+...+5^{10}\left(5+5^2\right)\)
\(=30\left(1+5^2+...+5^{10}\right)⋮30\)
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a: Sửa đề: S=5+5^2+...+5^2006
5S=5^2+5^3+...+5^2007
=>4S=5^2007-5
=>S=(5^2007-5)/4
b: S=5+5^4+5^2+5^5+...+5^2003+5^2006
=5(1+5^3)+5^2(1+5^3)+...+5^2003(1+5^3)
=126(5+5^2+...+5^2003) chia hết cho 126
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a/
\(\dfrac{2n+9}{n+1}=\dfrac{2\left(n+1\right)+7}{n+1}=2+\dfrac{7}{n+1}\)
\(\Rightarrow n+1=\left\{-7;-1;1;7\right\}\Rightarrow n=\left\{-8;-2;0;6\right\}\)
b/
\(\dfrac{3n+5}{n-1}=\dfrac{3\left(n-1\right)+8}{n-1}=3+\dfrac{8}{n-1}\)
\(\Rightarrow n-1=\left\{-8;-4;-2;-1;1;2;4;8\right\}\)
\(\Rightarrow n=\left\{-7;-3;-1;0;2;5;9\right\}\)
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a; a - b ⋮ 6
a - b + 12b ⋮ 6
a + 11b ⋮ 6 (đpcm)
b; a - b ⋮ 6
a - b - 12a ⋮ 6
-11a - b ⋮ 6
-(11a + b) ⋮ 6
11a + b ⋮ 6 (đpcm)
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TL:
Ta có:
10 có mũ bao nhiêu đi nữa, thì + 109 hay 108 +..v.v
Thì số cuối của dãy số vẫn băng 0 nên
=> 109+108+107 chia hết cho 2
Học Tốt👍
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=4+3^2+3^3+...+3^{223}=3^0+3^1+3^2+3^3+...+3^{223}\)
=> \(3S=3+3^2+3^3+3^4+...+3^{224}\)
=> \(3S-S=3^{224}-1\)
=> \(S=\frac{3^{224}-1}{2}=\frac{\left(3^8\right)^{28}-1}{2}\)là số tự nhiên
Ta có: \(\left(3^8\right)^{28}-1⋮\left(3^8-1\right)\)
mà \(3^8-1=6560=41.160⋮41\)
=> \(\left(3^8\right)^{28}-1⋮41;\left(41;2\right)=1\)
=> \(S=\frac{\left(3^8\right)^{28}-1}{2}\) chia hết cho 41.
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Ta có : \(\text{n + 5 = (n - 1)+6}\)
Vì \(\text{(n-1) ⋮ n-1}\)
Nên để \(\text{n+5 ⋮ n-1}\)⋮ `n-1`
Thì \(\text{6 ⋮ n-1}\)
\(\Rightarrow\) \(\text{n - 1 ∈ Ư(6)}\)
\(\Rightarrow\) \(\text{n - 1 ∈}\) \(\left\{\text{±1;±2;±3;±6}\right\}\)
\(\Rightarrow\) \(\text{n ∈}\) \(\left\{\text{0;-1;-2;-5;2;3;4;7}\right\}\) \(\text{( TM )}\)
\(\text{________________________________________________________}\)
b, Ta có : \(\text{2n-4 = (2n+4)- 8 = 2(n+2) - 8}\)
Vì \(\text{2(n+2) ⋮ n+2}\)
Nên để \(\text{2n-4 ⋮ n+2}\)
Thì \(\text{8 ⋮ n+2}\)
\(\Rightarrow\) \(\text{n + 2 ∈ Ư(8)}\)
\(\Rightarrow\) \(\text{n + 2 ∈}\) \(\left\{\text{±1;±2;±4;±8}\right\}\)
\(\Rightarrow\) \(\text{n ∈}\) \(\left\{\text{-3;-4;-6;-10;-1;0;2;6}\right\}\) ( TM )
\(\text{_________________________________________________________________ }\)
c, Ta có :\(\text{ 6n + 4 = (6n + 3) +1 = 3(2n+1) + 1}\)
Vì \(\text{3(2n+1) ⋮ 2n+1}\)
Nên để\(\text{ 6n+4 ⋮ 2n+1}\)
Thì \(\text{1 ⋮ 2n+1}\)
\(\Rightarrow\) \(\text{2n + 1 ∈ Ư(1)}\)
\(\Rightarrow\) \(\text{2n + 1 ∈}\) \(\left\{\text{±1}\right\}\)
\(\Rightarrow\) \(\text{2n ∈}\) \(\left\{\text{-2;0}\right\}\)
\(\Rightarrow\) \(\text{n ∈}\) \(\left\{\text{-1;0}\right\}\) ( TM )
\(\text{_______________________________________}\)
Ta có : \(\text{3 - 2n = -( 2n - 3 ) = -( 2n + 2 ) + 5 = -2( n+1)+5}\)
Vì \(\text{-2(n+1) ⋮ n+1}\)
Nên để \(\text{3-2n ⋮ n+1}\)
Thì\(\text{ 5 ⋮ n + 1}\)
\(\Rightarrow\) \(\text{n + 1 ∈}\) \(\left\{\text{±1;±5}\right\}\)
\(\Rightarrow\) \(\text{n ∈}\) \(\text{-2;-6;0;4}\) ( TM )
Ko cm dc bi de sai