计算(-1×1/2)+(-1/2*1/3)+...+(-1/2012*1/2013)
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:2024/07/27 10:11:18
计算(-1×1/2)+(-1/2*1/3)+...+(-1/2012*1/2013)
![计算(-1×1/2)+(-1/2*1/3)+...+(-1/2012*1/2013)](/uploads/image/z/10583840-56-0.jpg?t=%E8%AE%A1%E7%AE%97%28-1%C3%971%2F2%29%2B%28-1%2F2%2A1%2F3%29%2B...%2B%28-1%2F2012%2A1%2F2013%29)
原式=(-1)*[(1*1/2)+(1/2*1/3)+...+(1/2012*1/2013)]
=(-1)*[(1-1/2)+(1/2-1/3)+...+(1/2012-1/2013)]
=(-1)*(1-1/2013)
=-2012/2013
=(-1)*[(1-1/2)+(1/2-1/3)+...+(1/2012-1/2013)]
=(-1)*(1-1/2013)
=-2012/2013