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计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+.+1/(a+2012)(a+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：2024/07/16 01:29:44
计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+.+1/(a+2012)(a+2013)
计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+.+1/(a+2012)(a+2013)
原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3)+.+1/(a+2012)-1/(a+2013)
=1/a-1/(a+2013)
=2013/(a²+2013a)
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