作业帮计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+.+1/(a+2012)(a+2013)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 22:12:34
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)
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)
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)
=[(a+2013)-a]/[a(a+2013)]
=2013/[a(a+2013)]
=2013/(a²+2013a)
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1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+......+1/(a+2012)(a+2013)
=[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/a(a+2013)
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