作业帮计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]
来源：学生作业帮助网 编辑：作业帮 时间：2024/08/03 05:56:21
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计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]
计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]
计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]
原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)……+1/(a+2003)-1/(a+2004)
=1/a-1/(a+2004)
=2004/a(a+2004)
1/a(a+1)+.......=1/a-1/(a+1)+1/(a+1)-1/(a+2)+......+1/(a+2003)-1/(a+2004)=1/a-1/(a+2004)=2004/a(a+2004)
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