探究计算:1/(2乘以4)+1/(4乘以6)+…+1/(2010乘以2012)
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:2024/06/17 08:42:24
探究计算:1/(2乘以4)+1/(4乘以6)+…+1/(2010乘以2012)
1/(2乘以4)+1/(4乘以6)+…+1/(2010乘以2012)
=1/(2*2*1*2)+1/(2*2*2*3)+1/(2*2*3*4)+.1/(2*2*1005*1006)
=1/4[1/(1*2)+1/(2*3)+1/(3*4)+.1/(1005*1006)]
=1/4[1/1-1/2+1/2-1/3+1/3-1/4+.1/1005-1/1006]
=1/4(1005/1006)
=1/(2*2*1*2)+1/(2*2*2*3)+1/(2*2*3*4)+.1/(2*2*1005*1006)
=1/4[1/(1*2)+1/(2*3)+1/(3*4)+.1/(1005*1006)]
=1/4[1/1-1/2+1/2-1/3+1/3-1/4+.1/1005-1/1006]
=1/4(1005/1006)
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