Is the result of 2010-2009 + 2008-2007 +... + 2-1 odd or even

Is the result of 2010-2009 + 2008-2007 +... + 2-1 odd or even

2010-2009+2008-2007+...+2-1
=(2010-2009)+(2008-2007)+(2006-2005)…… +(2-1)
=1+1+1+…… +1
=2010÷2
=1005
So the result is odd