作业帮计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+···+1/(a+2004)(a+2005)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/12 13:05:57
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)
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)
1/n(n+1)=1/n-1/(n+1)
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+2004)-1/(a+2005)
=1/a-1/(a+2005)
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