(2009²-2008²)+(2007²-2006²)+（2005²-2004²）+·····+1²整式的化简,求用简便方法解

(2009²-2008²)+(2007²-2006²)+（2005²-2004²）+·····+1²整式的化简,求用简便方法解
(2009²-2008²)+(2007²-2006²)+（2005²-2004²）+·····+1²
整式的化简,求用简便方法解

(2009²-2008²)+(2007²-2006²)+（2005²-2004²）+·····+1²整式的化简,求用简便方法解
平方差
=(2009+2008)(2009-2008)+……+(2+1)(2-1)
=2009+2008……+2+1
=2010×2009÷2
=2019045