用简便算法计算.(1)2004+2003-2002-2001+2000+1999-1998-1997+...+8+7-6-5+4+3-2-1 = = =(2)2005×20062006-2006×20052005

问题描述:

用简便算法计算.(1)2004+2003-2002-2001+2000+1999-1998-1997+...+8+7-6-5+4+3-2-1 = = =
(2)2005×20062006-2006×20052005

=(2004-2002)+(2003-2001)+(2000-1998)+...+(8-6)+(7-5)+(4-2)+(3-1)=2004/2*2=2004

(1)2004+2003-2002-2001+2000+1999-1998-1997+...+8+7-6-5+4+3-2-1
=(2004-2002)+(2003-2001)+(2000-1998)+...+(8-6)+(7-5)+(4-2)+(3-1)
= 2004/2 × 2
= 2004
(2)2005×20062006-2006×20052005
= 2005 × (20060000 + 2006)- 2006 × (20050000 + 2005)
= 2005 × 2006 × (10000 + 1)- 2006 × 2005 × (10000 + 1)
= 2005 × 2006 × 10001 - 2006 × 2005 × 10001
= 0