计算:(1²-2²/1+2)+(2²-3²/2+3)+…+(99²-1
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/08/09 19:06:59
计算:(1²-2²/1+2)+(2²-3²/2+3)+…+(99²-100²/99+100).
![计算:(1²-2²/1+2)+(2²-3²/2+3)+…+(99²-1](/uploads/image/z/6181485-69-5.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BC%881%26%23178%3B-2%26%23178%3B%2F1%2B2%EF%BC%89%2B%EF%BC%882%26%23178%3B-3%26%23178%3B%2F2%2B3%EF%BC%89%2B%E2%80%A6%2B%EF%BC%8899%26%23178%3B-1)
(1²-2²/1+2)+(2²-3²/2+3)+…+(99²-100²/99+100)
=[(1-2)(1+2)/(1+2)+(2-3)(2+3)/(2+3)+…+(99-100)(99+10)/(99+100)]
=(1-2)+(2-3)+.+(99-100) 共计99组数
=(-1)*99
=-99
=[(1-2)(1+2)/(1+2)+(2-3)(2+3)/(2+3)+…+(99-100)(99+10)/(99+100)]
=(1-2)+(2-3)+.+(99-100) 共计99组数
=(-1)*99
=-99