2008-1/2008=2007/2008

1/2-1/2009=2007/2009

=(1-2-3+4)+(5-6-7+8)+...+(2005-2006-2007+2008)+2009

=2009

Số hạng của dãy là: (2009 - 1) : 2 + 1 = 1005 (Số)

Tổng của dãy đó là: (2009 + 1) x 1005 : 2 = 1 010 025

⇔ A = 1010025

Ta có : \(A=1+2+3+5+...+2009\)

\(=2+1+3+5+...+2009\)

Ta lại có : \(1+3+5+7+...=\dfrac{\left(2009+1\right).\left(\dfrac{2009-1}{2}+1\right)}{2}=1010025\)

\(\Rightarrow A=2+1010025=1010027\)

Vậy ...

`2007/2009×2002/2005×2009/2006×2005/2007×2006/2002`
`=(2007xx2002xx2009xx2005xx2006)/(2009xx2005xx2006xx2007xx2002)`
`=(2007xx2002xx2009xx2005xx2006)/(2007xx2002xx2009xx2005xx2006)`
`=1`

\(\dfrac{2007}{2009}.\dfrac{2002}{2005}.\dfrac{2009}{2006}.\dfrac{2005}{2007}.\dfrac{2006}{2002}\\ =\left(\dfrac{2007}{2009}.\dfrac{2009}{2006}\right).\left(\dfrac{2006}{2002}.\dfrac{2002}{2005}\right).\dfrac{2005}{2007}\\ =\dfrac{2007}{2006}.\dfrac{2006}{2005}.\dfrac{2005}{2007}=1\)

\(\dfrac{2007}{2009}\text{×}\dfrac{2002}{2005}\text{×}\dfrac{2009}{2006}\text{×}\dfrac{2005}{2007}\text{×}\dfrac{2006}{2002}\\ =\dfrac{2007\text{×}2002\text{×}2009\text{×}2005\text{×}2006}{2009\text{×}2005\text{×}2006\text{×}2007\text{×}2002}=1\)

1 - 3 + 5 - 7 + ... + 2001 - 2003 + 2005

= ( 1 - 3 ) + ( 5 - 7 ) + ... + ( 2001 - 2003 ) + 2005

= ( -2 ) + ( -2 ) + ... + ( -2 ) + 2005

= ( -2 ) . 501 + 2005

= ( -1002 ) + 2005

= 1003 

~ Hok tốt ~

1 - 3 + 5 - 7 + ... + 2005 - 2007 + 2009

= ( 1 - 3 ) + ( 5 - 7 ) + ... + ( 2005 - 2007 ) + 2009

= ( -2 ) + ( -2 ) + ... + ( -2 ) + 2009

= ( -2 ) . 502 + 2009

= ( -1004 ) + 2009

= 1005

~ Hok tốt ~

giúp em nốt câu này

1-2+3-4+5-6+...+99-100+101

a) (-1) + 2 + (-3) + 4 + .... + (-2009) + 2010

= (-1 + 2) + (-3 + 4) + ..... + (-2009 + 2010)

= -1 + (-1) + (-1) + .... + (-1) 

= -1 . 1005 = -1005

b) 1 + (-2) + (-3) + 4 + 5 + (-6) + (-7) + 8 + ... + 2005 + (-2006) + (-2007) + 2008

= [1 + (-2) + (-3) + 4] + [5 + (-6) + (-7) + 8 ] + ..... + [2005 + (-2006) + (-2007) + 2008]

= 0 + 0 + ...... + 0 = 0

ghe

a) Ta có: \(\left(-1\right)+2+\left(-3\right)+4+...+\left(-2009\right)+2010\)

\(=1+1+...+1\)

=1005

b) Ta có: \(1+\left(-2\right)+\left(-3\right)+4+5+\left(-6\right)+\left(-7\right)+8+...+2005+\left(-2006\right)+\left(-2007\right)+2008\)

\(=\left(1-2-3+4\right)+\left(5-6-7+8\right)+...+\left(2005-2006-2007+2008\right)\)

=0