计算:2006²-2005²+2004²-2003²+2002²-……+2²-1²
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 00:44:45
![计算:2006²-2005²+2004²-2003²+2002²-……+2²-1²](/uploads/image/z/169756-52-6.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A2006%26%23178%3B-2005%26%23178%3B%2B2004%26%23178%3B-2003%26%23178%3B%2B2002%26%23178%3B-%E2%80%A6%E2%80%A6%2B2%26%23178%3B-1%26%23178%3B)
计算:2006²-2005²+2004²-2003²+2002²-……+2²-1²
计算:2006²-2005²+2004²-2003²+2002²-……+2²-1²
计算:2006²-2005²+2004²-2003²+2002²-……+2²-1²
利用a²-b²=(a+b)(a-b)
2006²-2005²+2004²-2003²+2002²-……+2²-1²
=(2006+2005)(2006-2005)+(2004+2003)(2004-2003)+……+(2+1)(2-1)
=2006+2005+2004+2003+……+2+1
=(1+2006)×2006÷2
=2013021