cm \(3^{2010}+5^{2015}\) chia hết cho 13
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b: B=3(1+3)+3^3(1+3)+...+3^2009(1+3)
=4(3+3^3+...+3^2009) chia hết cho 4
B=3(1+3+3^2)+3^4(1+3+3^2)+...+3^2008(1+3+3^2)
=13(3+3^4+...+3^2008) chia hết cho 13
c: \(C=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{2009}\left(1+5\right)\)
\(=6\left(5+5^3+...+5^{2009}\right)⋮6\)
\(C=5\left(1+5+5^2\right)+5^4\left(1+5+5^2\right)+...+5^{2008}\left(1+5+5^2\right)\)
\(=31\left(5+5^4+...+5^{2008}\right)⋮31\)
d: \(D=7\left(1+7\right)+7^3\left(1+7\right)+...+7^{2009}\left(1+7\right)\)
\(=8\left(7+7^3+...+7^{2009}\right)⋮8\)
\(D=7\left(1+7+7^2\right)+7^4\left(1+7+7^2\right)+...+7^{2008}\left(1+7+7^2\right)\)
\(=57\left(7+7^4+...+7^{2008}\right)⋮57\)
Bài 1:
ta có 3^3 = 27 chia 13 dư 1
=> (3^3)^670 = 3^ 2010 chia 13 dư 1 (1)
5^2 = 25 chia 13 dư (-1)
=> (5^2)^1005 chia 13 dư (-1)^ 1005 = (-1) (2)
Từ (1); (2)
=> 3^2010+5^2010 chia 13 dư 1 + (-1) = 0
hay 3^2010+5^2010 chia hết cho 13.
=(1+3+32)+(33+34+35)+...+(32013+32014+32015)
=(1+3+32)+33(1+3+32)+...+32013(1+3+32)
=13(1+33+...+32013) chia hết cho 13(đpcm)
= (1+3+32) +(33+34+35)+.....+(32013+32014+32015)
=(1+3+32) + 33+(1+3+32) +...+32013(1+3+32)
=13(1+33+...+32015) chia hét cho 13
nhanh nhất đấy
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Bài 1:
$A=2^1+2^2+2^3+2^4$
$2A=2^2+2^3+2^4+2^5$
$\Rightarrow 2A-A=2^5-2^1$
$\Rightarrow A=2^5-1=32-1=31$
----------------------------
$B=3^1+3^2+3^3+3^4$
$3B=3^2+3^3+3^4+3^5$
$\Rightarrow 3B-B = 3^5-3$
$\Rightarrow 2B = 3^5-3\Rightarrow B = \frac{3^5-3}{2}$
--------------------------
$C=5^1+5^2+5^3+5^4$
$5C=5^2+5^3+5^4+5^5$
$\Rightarrow 5C-C=5^5-5$
$\Rightarrow C=\frac{5^5-5}{4}$
A=2^1+2^2+2^3+2^4+...+2^2010
=(2+2^2)+(2^3+2^4)+...+(2^2010+2^2011)
=2.(1+2)+2^3.(1+2)+...+2^2010.(1+2)
=2.3+2^3.3+...+2^2010.3
=(2+2^3+2^2010).3
=> A chia het cho 3
ta có: 32010 + 52010 = (33)670 + (52)1005 = 27670 + 251005 = (26 + 1)670 + (26 - 1)1005 = 26A + 1670 - 11005 = 26A chia hết cho 13
=> 32010 + 52010 chia hết cho 13
t i c k nha!!! 6756845645765576599435256344465757686878976
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