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\(6+6^2+\cdot\cdot\cdot+6^{10}\)
\(=6\cdot\left(1+6\right)+6^3\cdot\left(1+6\right)+\cdot\cdot\cdot+6^9\cdot\left(1+6\right)\)
\(=6\cdot7+6^3\cdot7+\cdot\cdot\cdot+6^9\cdot7\)
\(=7\cdot\left(6+6^3+\cdot\cdot\cdot+6^9\right)⋮7\)
\(\Rightarrow6+6^2+\cdot\cdot\cdot\cdot+6^{10}⋮7\)
A = 2 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 210
A = (2 + 22) + (23 + 24) + (25 + 26) + (27 + 28) + (29 + 210)
A = 2(1 + 2) + 23(1 + 2) + 25(1 + 2) + 27(1 + 2) + 29(1 + 2)
A = 2.3 + 23.3 + 25.3 + 27.3 + 29.3
A = (2 + 23 + 25 + 27 + 29) . 3
Mà 3 ⋮ 3
⇔ A ⋮ 3
Câu 2;3;4 dễ quá... bỏ qua!!
Câu 5;6 khó quá ... khỏi làm!!
dễ quá bỏ qua!!, khó quá khỏi làm!!
cứ tiêu chí mày bạn sẽ vượt qua mọi bài toán... và nhanh chóng đạt 1đ.
\(A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+\left(2^5+2^6\right)+\left(2^7+2^8\right)+\left(2^9+2^{10}\right)\)
\(A=2\left(1+2\right)+2^3\left(1+2\right)+2^5\left(1+2\right)+2^7\left(1+2\right)+2^9\left(1+2\right)\)
\(A=2\cdot3+2^3\cdot3+2^5\cdot3+2^7\cdot3+2^9\cdot3\text{ }⋮\text{ }3\)
\(A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+\left(2^5+2^6\right)+\left(2^7+2^8\right)+\left(2^9+2^{10}\right)\)
\(A=2\left(1+2\right)+2^3\left(1+2\right)+2^5\left(1+2\right)+2^7\left(1+2\right)+2^9\left(1+2\right)\)
\(A=2\cdot3+2^3\cdot3+2^5\cdot3+2^7\cdot3+2^9\cdot3\)
\(\Rightarrow\text{ }A\text{ }⋮\text{ }3\text{ }\left(\text{ ĐPCM}\right)\)
\(\text{}A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+\left(2^5+2^6\right)+\left(2^7+2^8\right)+\left(2^9+2^{10}\right)\)
\(=2.\left(1+2\right)+2^3.\left(1+2\right)+2^5.\left(1+2\right)+2^7.\left(1+2\right)+2^9.\left(1+2\right)\)
\(=2.3+2^3.3+2^5.3+2^7.3+2^9.3\)
\(=3\left(2+2^3+2^5+2^7+2^9\right)\)
Thấy : \(2+2^3+2^5+2^7+2^9\in N\)
\(\Rightarrow3\left(2+2^3+2^5+2^7+2^9\right)⋮3\)
Hay : \(A⋮3\)( đpcm )
A = 2 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 210
A = ( 2 + 22 ) + ( 23 + 24 ) + ( 25 + 26 ) + ( 27 + 28 ) + ( 29 + 210 )
A = 2.( 1 + 2 ) + 23.( 1 + 2 ) + 25.( 1 + 2 ) + 27.( 1 + 2 ) + 29.( 1 + 2 )
A = 2.3 + 23.3 + 25. 3 + 27.3 + 29.3
A = 3.( 2 + 23 + 25 + 27 + 29 ) \(⋮\)3
Vậy A chia hết cho 3.