2014²-2013²+2012²-2011²+···+2²-1²
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 16:25:53
![2014²-2013²+2012²-2011²+···+2²-1²](/uploads/image/z/5304314-2-4.jpg?t=2014%26%23178%3B-2013%26%23178%3B%2B2012%26%23178%3B-2011%26%23178%3B%2B%C2%B7%C2%B7%C2%B7%2B2%26%23178%3B-1%26%23178%3B)
2014²-2013²+2012²-2011²+···+2²-1²
2014²-2013²+2012²-2011²+···+2²-1²
2014²-2013²+2012²-2011²+···+2²-1²
=(2014+2013)(2014-2013)+(2012+2011)(2012-2011)+……+(2+1)(2-1)
=2014+2013+2012+2011+……+2+1
=2014*1+2014(2014-1)*1/2
=2014+1007*2013
=2029105