\(\frac{2009\times2010-1}{2008\times2010+2009}\)
Những câu hỏi liên quan
Tìm \(x\):
\(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+.....\frac{1}{2009\times2010}\right)\times x=2009\)
\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+....+\frac{1}{2009\cdot2010}\right)\cdot x=2009\)
\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\right)\cdot x=2009\)
\(\left(1-\frac{1}{2010}\right)\cdot x=2009\)
\(\frac{2009}{2010}\cdot x=2009\)
\(x=2009:\frac{2009}{2010}\)
\(x=2010\)
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\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+....+\frac{1}{2009}-\frac{1}{2010}\right).x=2009\)
\(\left(\frac{1}{1}-\frac{1}{2010}\right).x=2009\)
\(\frac{2009}{2010}.x=2009\)
\(x=2009:\frac{2009}{2010}\)
\(x=2010\)
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so sánh già trị các biểu thức sau
\(A=\frac{2011\times2012}{2011+2012}+\frac{2009\times2010}{2009+2010}\)
\(B=\frac{2011\times2011}{2011+2012}+\frac{2010\times2010}{2009+2010}\)
\(A=\frac{2011\times2012}{2011+2012}+\frac{2009\times2010}{2009+2010}\)
\(A=\frac{2011\times2011}{2011+2012}+\frac{2011}{2011+2012}+\frac{2010\times2010}{2009+2010}-\frac{2010}{2009+2010}\)
\(A=\frac{2011\times2011}{2011+2012}+\frac{2010\times2010}{2009+2010}+\frac{2011}{2011+2012}-\frac{2010}{2009+2010}\)
\(A=B+\frac{2011}{2011+2012}-\frac{2010}{2009+2010}\)
\(A=B+\frac{2011}{4023}-\frac{2010}{4019}\)
Dễ thấy \(\frac{2011}{4023}-\frac{2010}{4019}< 0\)
\(\Rightarrow A< B\)
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tính nhanh
\(8\times2010\times125-2009\times437-2009\times563\)
8 x 2010 x 125 - 2009 x 437 - 2009 x 563
= ( 8 x 125 ) x 2010 - 2009 x ( 437 + 563 )
= 1000 x 2010 - 2009 x 1000
= 1000 x ( 2010 - 2009 )
= 1000 x 1
= 1000
=))
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8 x 2010 x 125 - 2009 x 437 - 2009 x 563 = 1000
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8 x 2010 x 125 - 2009 x 437 - 2009 x 563
(125 x 8) x 2010 - (2009 x 437 + 2009 x 563)
= 1000 x 2010 - [2009 x (437 + 563)]
= 1000 x 2010 - 2009 x 1000
= 1000 x (2010 - 2009)
= 1000 x 1
= 1000
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Xem thêm câu trả lời
\(\dfrac{2011-6033\div\left(y-2010\right)}{2009\times2010\times2013}\)
Tìm x biết \(\frac{4}{2\times4}+\frac{4}{4\times6}+\frac{4}{6\times8}+...+\frac{4}{2008\times2010}+x=\frac{-1}{1005}\)
\(\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+...+\frac{4}{2008\cdot2010}+x=-\frac{1}{1005}\)
\(2\cdot\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{2008\cdot2010}\right)+x=-\frac{1}{1005}\)
\(2\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)+x=-\frac{1}{1005}\)
\(2\cdot\left[\left(\frac{1}{2}-\frac{1}{2010}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{6}-\frac{1}{6}\right)+...+\left(\frac{1}{2008}-\frac{1}{2008}\right)\right]+x=-\frac{1}{1005}\)\(2\cdot\left[\left(\frac{1005}{2010}-\frac{1}{2010}\right)+0+...+0\right]+x=-\frac{1}{1005}\)
\(2\cdot\frac{1004}{2010}+x=-\frac{1}{1005}\)
\(\frac{1004}{1005}+x=-\frac{1}{1005}\)
\(x=-\frac{1}{1005}-\frac{1004}{1005}=-1\)
Vậy x=-1
Chúc bạn học tốt!^_^
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Tính:
A = \(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+99\right)}{1\times99+2\times98+3\times97+...+99\times1}\)
B = \(\frac{1\times2010+2\times2009+3\times2008+...+2010\times1}{\left(1+2+3+...+2010\right)+\left(1+2+3+...+2009\right)+...+\left(1+2\right)+1}\)
cmr:
\(\frac{2009^{2008}-1}{2009^{2009}-1}< \frac{2009^{2007}+1}{2009^{2008}+1}\)
so sánh \(\frac{2009^{2008}+1}{2009^{2009}+1}\)và \(\frac{2009^{2008}+5}{2009^{2008}+9}\)
so sánh 2008 với tổng 2009 số hạng sau\(s=\frac{2008+2007}{2009+2008}+\frac{^{2008^2+2007^2}}{2009^2+2008^2}+.....+\frac{2008^{2009}+2007^{2009}}{2009^{2009}+2008^{2009}}\)