求 2012²-2011²+2010²-2009 ²+…+4²-3²+2²-1等于多少
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![求 2012²-2011²+2010²-2009 ²+…+4²-3²+2²-1等于多少](/uploads/image/z/673458-42-8.jpg?t=%E6%B1%82+2012%26%23178%3B-2011%26%23178%3B%2B2010%26%23178%3B-2009+%26%23178%3B%2B%E2%80%A6%2B4%26%23178%3B-3%26%23178%3B%2B2%26%23178%3B-1%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91)
求 2012²-2011²+2010²-2009 ²+…+4²-3²+2²-1等于多少
求 2012²-2011²+2010²-2009 ²+…+4²-3²+2²-1等于多少
求 2012²-2011²+2010²-2009 ²+…+4²-3²+2²-1等于多少
2012²-2011²+2010²-2009²+…+4²-3²+2²-1
=(2012²-2011²)+(2010²-2009²)+…+(4²-3²)+(2²-1)
=(2012+2011)(2012-2011)+(2010+2009)(2010-2009)+...+(4+3)(4-3)+(2+1)(2-1)
=2012+2011+2010+2009+...+4+3+2+1
=(2012+1)X2012/2
=2025078