2008²-2007²+2006²-2005²+﹍+2²-1
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 00:59:23
![2008²-2007²+2006²-2005²+﹍+2²-1](/uploads/image/z/346808-56-8.jpg?t=2008%26%23178%3B-2007%26%23178%3B%EF%BC%8B2006%26%23178%3B-2005%26%23178%3B%2B%EF%B9%8D%2B2%26%23178%3B-1)
2008²-2007²+2006²-2005²+﹍+2²-1
2008²-2007²+2006²-2005²+﹍+2²-1
2008²-2007²+2006²-2005²+﹍+2²-1
2008²-2007²+2006²-2005²+﹍+2²-1
=(2008+2007)(2008-2007)+(2006+2005)(2006-2005)+...+(2+1)(2-1)
=2008+2007+2006+2005+...+2+1
=2008*2009/2
=2017036
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2008²-2007²+2006²-2005²+﹍+2²-1
=(2008²-2007²)+(2006²-2005²)+……+(2²-1)
=2008+2007+2006+2005+……+2+1
=(2008+1)*2008/2
=2009*1004
=2017036