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计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+···+1/(a+2004)(a+2005)

来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：数学作业 时间：2024/05/15 03:53:04
计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+···+1/(a+2004)(a+2005)
计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+···+1/(a+2004)(a+2005)
1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+···+1/(a+2004)(a+2005)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3)+---+1/(a+2004)-1/(a+2005)
=1/a-1/(a+2005)
=2005/(a²+2005a)
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