HS
4
K
Khách
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D
25 tháng 2 2020
a, \(17.201-7.201-2009\\ =\left(17-7\right).201-2009\\ =10.201-2009\\ =2010-2009\\ =1\)
b, \(73.\left(-12\right)+\left(-73\right).88\\ =73.\left(-12\right)+73.\left(-88\right)\\ =73.\left[\left(-12\right)+\left(-88\right)\right]\\ =73.\left(-100\right)\\ =-7300\)
c, \(\frac{6}{25}+\left(-\frac{2}{18}\right)+\frac{19}{25}+\left(-\frac{8}{9}\right)\\ =\left(\frac{6}{25}+\frac{19}{25}\right)+\left(-\frac{2}{18}\right)+\left(-\frac{16}{18}\right)\\ =\frac{25}{25}+\left[\left(-\frac{2}{18}\right)+\left(-\frac{16}{18}\right)\right]\\ =1+\left(-\frac{18}{18}\right)\\ =1+\left(-1\right)\\ =0\)
2 tháng 6 2015
Dễ quá, thực hiện qui tắc bỏ dấu ngoặc được:
\(2009+2009^2+....+2009^{2009}-1-2009-...-2009^{2008}\)
\(=-1+\left(2009-2009\right)+\left(2009^2-2009^2\right)+...+\left(2009^{2008}-2009^{2008}\right)+2009^{2008}\)
\(=2009^{2008}-1\)
\(=\left(2009-1\right)\left(2009^{2007}+2009^{2008}+...+2009+1\right)\)
\(=2008\left(2009^{2007}+2009^{2008}+...+2009+1\right)\) chia hết cho 2008
=> ĐPCM
VT
2 tháng 6 2015
Chứng Minh Rằng: (2009+20092+20093+20094+...+20092009)-(1+2009+20092+20093+...+20092008) chia hết cho 2008.
Đặt A=2009+20092+20093+20094+...+20092009, B=1+2009+20092+20093+20094+...+20092008
Ta có:
+)A=2009+20092+20093+20094+...+20092009
2009A= 20092+20093+20094+...+20092010
2009A-A=(20092+20093+20094+...+20092010)-(2009+20092+20093+20094+...+20092009)
2008A=20092010- 2009
=> A=(20092010- 2009)/2008
=> A chia hết cho 2008.
B=1+2009+20092+20093+20094+...+20092008
2009B=2009+20092+20093+20094+...+20092010
2009B-B=(2009+20092+20093+20094+...+20092010)-(1+2009+20092+20093+20094+...+20092009)
2008B=20092010-1
=>B=(20092010-1)/2008
=>B chia hết cho 2008
=> A-B chia hết cho 2008.
=> ĐPCM
NT
2
6 tháng 2 2017
( - 2009 - 2009 - 2009 - 2009 ) . ( - 25 )
= 2009 + 2009 + 2009 + 2009 . ( - 25 )
= 2009 . 4 . ( - 25 )
= 2009 . [ 4 . ( - 25 ) ]
= 2009 . ( - 100 )
= - 200 900
HM
2
S
10 tháng 10 2016
Đặt \(A=\frac{2009^{2008}+1}{2009^{2009}+1}\)và \(B=\frac{2009^{2009}+1}{2009^{2010}+1}\)
\(A=\frac{2009^{2008}+1}{2009^{2009}+1}\Rightarrow2009A=\frac{2009.\left(2009^{2008}+1\right)}{2009^{2009}+1}=\frac{2009^{2009}+2009}{2009^{2009}+1}=1+\frac{2008}{2009^{2009}+1}\)
\(B=\frac{2009^{2009}+1}{2009^{2010}+1}\Rightarrow2009B=\frac{2009.\left(2009^{2009}+1\right)}{2009^{2010}+1}=\frac{2009^{2010}+2009}{2009^{2010}+1}=1+\frac{2008}{2009^{2010}+1}\)
Vì \(\frac{2008}{2009^{2009}+1}>\frac{2008}{2009^{2010}+1}\Rightarrow2009A>2009B\Rightarrow A>B\)
NT
4
DV
0
TL
0
29 tháng 6 2017
\(2009A=\frac{2009^{2010}+2009}{2009^{2010}+1}=\)\(\frac{2009^{2010}+1+2008}{2009^{2010}+1}=1+\frac{2008}{2009^{2010}+1}\)
\(2009B=\frac{2009^{2009}+2009}{2009^{2009}+1}=\frac{2009^{2009}+1+2008}{2009^{2009}+1}\)\(=1+\frac{2008}{2009^{2009}+1}\)
Vì \(1+\frac{2008}{2009^{2010}+1}< 1+\frac{2008}{2009^{2009}+1}\) \(\Leftrightarrow A< B\)
29 tháng 6 2017
\(A=\frac{2009^{2009}+1}{2009^{2010}+1}\Rightarrow2009A=\frac{2009^{2010}+2009}{2009^{2010}+1}\)
\(2009A=\frac{2009^{2010}+1}{2009^{2010}+1}+\frac{2008}{2009^{2010}+1}\)
\(2009A=1+\frac{2008}{2009^{2010}+1}\)
..... sory bn mk hơi luwoif chút nên bn tự lm tương tự vs phần B và so sánh nhé!^^
SM
2
MV
22 tháng 4 2017
B = \(\dfrac{2009^{2009}+1}{2009^{2010}+1}\)<\(\dfrac{2009^{2009}+1+2008}{2009^{2010}+1+2008}\)=\(\dfrac{2009^{2009}+2009}{2009^{2010}+2009}\)=\(\dfrac{2009.\left(2009^{2008}+1\right)}{2009.\left(2009^{2009}+1\right)}\)=\(\dfrac{2009^{2008}+1}{2009^{2019}+1}\)= A
Vậy A > B
22 tháng 4 2017
Ta có :
\(2009A=\dfrac{2009^{2009}+2009}{2009^{2009}+1}=\dfrac{2009^{2009}+1+2008}{2009^{2009}+1}=\dfrac{2009^{2009}+1}{2009^{2009}+1}+\dfrac{2008}{2009^{2009}+1}=1+\dfrac{2008}{2009^{2009}+1}\)
\(2009B=\dfrac{2009^{2010}+2009}{2009^{2010}+1}=\dfrac{2009^{2010}+1+2008}{2010^{2010}+1}=\dfrac{2009^{2010}+1}{2009^{2010}+1}+\dfrac{2008}{2009^{2010}+1}=1+\dfrac{2008}{2009^{2010}}\)
\(\)Vì \(1+\dfrac{2008}{2009^{2009}+1}>1+\dfrac{2008}{2009^{2010}+1}\Rightarrow A>B\)
~ Học tốt ~
=201x(17-7)-2009
=201x10-2009
=2010-2009
=1
17.201-7.201-2009
=201(17-7)-2009
=201.10-2009
=2010-2009=1
Học tốt!
#Huyền#