Chứng minh rằng:
\(2005^{2007}+2007^{2005}⋮2006\)
LK
Những câu hỏi liên quan
\(A=2005^{2007^{2006}}+2006^{2005^{2007}}+2007^{2006^{2005}}\)
Chứng minh rằng A chia hết cho 102( lưu ý không sử dụng đồng dư thức để chứng minh)
Cho frac{a}{b}frac{c}{d}. Chứng minh:a) frac{left(a-bright)^3}{left(c-dright)^3}frac{3a^2+2b^2}{3c^2+2d^2}b)frac{4a^4+5b^4}{4c^4+5d^4}frac{a^2b^2}{c^2d^2}c)left(frac{a-b}{c-d}right)^{2005}frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}d)frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}frac{left(a+bright)^{2005}}{left(c+dright)^{2005}}e)frac{left(20a^{2006}+11b^{2006}right)^{2007}}{left(20a^{2007}-11b^{2007}right)^{2006}}frac{left(20c^{2006}+11d^{2006}right)^{2007}}{left(20c^{2007}-11d^{2007}right)^{20...
Đọc tiếp
Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh:
a) \(\frac{\left(a-b\right)^3}{\left(c-d\right)^3}=\frac{3a^2+2b^2}{3c^2+2d^2}\)
b)\(\frac{4a^4+5b^4}{4c^4+5d^4}=\frac{a^2b^2}{c^2d^2}\)
c)\(\left(\frac{a-b}{c-d}\right)^{2005}=\frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}\)
d)\(\frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}=\frac{\left(a+b\right)^{2005}}{\left(c+d\right)^{2005}}\)
e)\(\frac{\left(20a^{2006}+11b^{2006}\right)^{2007}}{\left(20a^{2007}-11b^{2007}\right)^{2006}}=\frac{\left(20c^{2006}+11d^{2006}\right)^{2007}}{\left(20c^{2007}-11d^{2007}\right)^{2006}}\)
f)\(\frac{\left(20a^{2007}-11c^{2007}\right)^{2006}}{\left(20a^{2006}+11c^{2006}\right)^{2007}}=\frac{\left(20b^{2007}-11d^{2007}\right)^{2006}}{\left(20b^{2006}+11d^{2006}\right)^{2007}}\)
ừ, bạn bik làm thì giúp mình nha ^^
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Chứng minh rằng : 2.4.6. ... .2006 + 1.3.5. ... .2005 chia hết cho 2007
So sánh A và B :
a, A = 2006^2006 + 1 / 2006^2007 + 1 và B = 2006^2007 + 1 / 2006^2008 + 1
b, A = 2004 . 2005 - 1 / 2004 . 2005 và B = 2005 . 2006 - 1 / 2005 . 2006
CHO a/b c/d . Chứng minh1) a2004- b2004 / a2004 + b2004 c2004- d2004 / c2004 + d20042) (a2004+ b 2004) 2005/(c2004+d2004) 2005 (a2005 - b 2005) 2004/ (c2005 - d2005) 20043) (20a2006 +11b2006) 2007 /(20a200711b2007) 2006 (20c2006+ 11d2006) 2007 / (20c2007- 11d 2007)2006
Đọc tiếp
CHO a/b = c/d . Chứng minh
1) a2004- b2004 / a2004 + b2004 = c2004- d2004 / c2004 + d2004
2) (a2004+ b 2004) 2005/(c2004+d2004) 2005 = (a2005 - b 2005) 2004/ (c2005 - d2005) 2004
3) (20a2006 +11b2006) 2007 /(20a200711b2007) 2006
= (20c2006+ 11d2006) 2007 / (20c2007- 11d 2007)2006
Chứng minh S=2.4.6.....2006+1.3.5.....2005 chia hết cho 2007
tính a
2005/2006+2006/2007+2007/2008+2008/2005
2005/2006 + 2006/2007 + 2007/2008 + 2008/2005
= 4,000001491
k minh di xin day
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minh ko bietcach giai tra loi giup minh di ban minh can gap
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tính giá trị của biểu thức 2007/2009×2002/2005×2009/2006×2005/2007×2006/2002
`2007/2009×2002/2005×2009/2006×2005/2007×2006/2002`
`=(2007xx2002xx2009xx2005xx2006)/(2009xx2005xx2006xx2007xx2002)`
`=(2007xx2002xx2009xx2005xx2006)/(2007xx2002xx2009xx2005xx2006)`
`=1`
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\(\dfrac{2007}{2009}.\dfrac{2002}{2005}.\dfrac{2009}{2006}.\dfrac{2005}{2007}.\dfrac{2006}{2002}\\ =\left(\dfrac{2007}{2009}.\dfrac{2009}{2006}\right).\left(\dfrac{2006}{2002}.\dfrac{2002}{2005}\right).\dfrac{2005}{2007}\\ =\dfrac{2007}{2006}.\dfrac{2006}{2005}.\dfrac{2005}{2007}=1\)
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\(\dfrac{2007}{2009}\text{×}\dfrac{2002}{2005}\text{×}\dfrac{2009}{2006}\text{×}\dfrac{2005}{2007}\text{×}\dfrac{2006}{2002}\\ =\dfrac{2007\text{×}2002\text{×}2009\text{×}2005\text{×}2006}{2009\text{×}2005\text{×}2006\text{×}2007\text{×}2002}=1\)
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so sánh tổng A với 3
A= 2005/2006+2006/2007+2007/2005
giúp tui nhé tui cần
Ta có: \(A=\dfrac{2005}{2006}+\dfrac{2006}{2007}+\dfrac{2007}{2005}=\dfrac{2006-1}{2006}+\dfrac{2007-1}{2007}+\dfrac{2005}{2005}+\dfrac{1}{2005}+\dfrac{1}{2005}\)\(=1+1+1+\left(\dfrac{1}{2005}-\dfrac{1}{2006}+\dfrac{1}{2005}-\dfrac{1}{2007}\right)\)
\(=3+\left(\dfrac{1}{2005}-\dfrac{1}{2006}+\dfrac{1}{2005}-\dfrac{1}{2007}\right)\)
Ta thấy: \(\dfrac{1}{2005}>\dfrac{1}{2006};\dfrac{1}{2005}>\dfrac{1}{2007}\) \(\Rightarrow\dfrac{1}{2005}-\dfrac{1}{2006}+\dfrac{1}{2005}-\dfrac{1}{2007}>0\)
\(\Rightarrow A>3\)
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