2012²-2011²+2010²-2009²……2²-1这道题怎么解啊
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 07:45:32
![2012²-2011²+2010²-2009²……2²-1这道题怎么解啊](/uploads/image/z/437906-2-6.jpg?t=2012%26%23178%3B-2011%26%23178%3B%2B2010%26%23178%3B-2009%26%23178%3B%E2%80%A6%E2%80%A62%26%23178%3B-1%E8%BF%99%E9%81%93%E9%A2%98%E6%80%8E%E4%B9%88%E8%A7%A3%E5%95%8A)
2012²-2011²+2010²-2009²……2²-1这道题怎么解啊
2012²-2011²+2010²-2009²……2²-1这道题怎么解啊
2012²-2011²+2010²-2009²……2²-1这道题怎么解啊
2012²-2011²+2010²-2009²+……+2²-1
=(2012+2011)(2012-2011)+(2010+2009)(2010-2009)+……+(2+1)(2-1)
=2012+2011+2010+2009+……+4+3+2+1
=(1+2012)×2012÷2
=2025078
2012²-2011²+2010²-2009²+……+2²-1
=(2012+2011)(2012-2011)+(2010+2009)(2010-2009)+……+(2+1)(2-1)
=2012+2011+2010+2009+……+4+3+2+1
=(1+2012)×2012÷2
=2025078
=(2012-2011)(2012+2011)+(2010-2009)(2010+9009)...........(2-1)(2+1)
=2012+2011+2010+2009......+2+1
=(2012+1)×2012/2
利用平方差
2012²-2011²+2010²-2009²+……+2²-1
=(2012+2011)(2012-2011)+(2010+2009)(2010-2009)+……+(2+1)(2-1)
=2012+2011+2010+2009+……+4+3+2+1
=(1+2012)×2012÷2
=2025078
答案满意,请帮我设置为采纳,谢谢!