Ta có:
\(3^{2005}+3^{2006}+3^{2007}+3^{2008}+3^{2009}\)
\(=3^0.3^{2005}+3^1.3^{2005}+3^2.3^{2005}+3^3.3^{2005}\) \(+3^4.3^{2005}\)
\(=3^{2005}\left(3^0+3^1+3^2+3^3+3^4\right)\)
\(=3^{2005}.121=3^{2005}.11.12⋮11\)
Vậy \(3^{2005}+3^{2006}+3^{2007}+3^{2008}+3^{2009}⋮11\) (Đpcm)
tính số hữu tỉ \(\frac{A}{B}biết:A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}B=\frac{2008}{1}+\frac{2007}{1}+\frac{2006}{1}+...+\frac{2}{2007}+\frac{1}{2008}.\)
So sánh: x = 2006/2007 - 2007/2008 + 2008/2009 - 2009/2010.
y = - 1/(2006 × 2007) - 1/(2007 × 2008).
x+1/2009 + x+2/2008 + x+3/2007 + x=10/2000 + x==11/1999 + x+12/1998
x-1 /2009+x-2.2008=x-3/2007+x-4/2006
So sánh
\(A=\frac{2^{2008}-3}{2^{2007}-1}\) và \(B=\frac{2^{2007}-3}{2^{2006}-1}\)
chứng minh rằng
1. (10^10 +10^16+ 10^17)chia hết cho 555
2.(84^7- 27^9 -9^13) chia hết cho 15
3. (5^7-5^6+5^5)chia hết cho 21
4. (7^6+7^5-7^4) chia hết cho 77
5.(4^13+ 32^5-8^8) chia hết cho 5
6.(2006^1000 +2006^999) chia hết cho 2007
7.(43^43 -17^17) chia hết cho 10
8. (7^1000- 3^1000) chia hết cho 10
9( 3^2016 +3^ 2015 - 3^2014)chia hết cho 11
10.(36^36 -9^10)chia hết cho 45
Khai triển và thu gọn 2 đa thức \(f\left(x\right)=\left(x-2\right)^{2008}+\left(2x-3\right)^{2007}+2006x\) và \(g\left(x\right)=y^{2009}-2007y^{2008}+2005y^{2007}\)
Tìm x biết :
a)2x+1)4 = (2x+1)6
b)\(\left|\left|x+3\right|-8\right|=20\)
c) \(\dfrac{x-1}{2009}+\dfrac{x-2}{2008}=\dfrac{x-3}{2007}+\dfrac{x-4}{2006}\)
Tìm x,y
a . (x+ 4/ 2007)+ (x+3/2008)=(x+2/2009)+(x+1/2010)
b . 2x+1 . 3y-2 = 12x
