计算: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:2024/08/02 06:21:28
计算:a(a+1) +1/(a+1)(a+2) +1/(a+2)(a+3) + +1/(a+2004)(a+2005)
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计算:a(a+1) +1/(a+1)(a+2) +1/(a+2)(a+3) + +1/(a+2004)(a+2005)
计算:a(a+1) +1/(a+1)(a+2) +1/(a+2)(a+3) + +1/(a+2004)(a+2005)

计算:a(a+1) +1/(a+1)(a+2) +1/(a+2)(a+3) + +1/(a+2004)(a+2005)
1/(a+1)(a+2)=1/(a+1)-1/(a+2)
同理:1/(a+2)(a+3)=1/(a+2)-1/(a+3)
所以:a(a+1) +1/(a+1)(a+2) +1/(a+2)(a+3) + +1/(a+2004)(a+2005)
=a(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3)+.+1/(a+2004)-1/(a+2005)
=a(a+1)+1/(a+1)-1/(a+2005)
希望你的第一项没写错,但愿是a/(a+1)
这样一来,答案就是1-1/(a+2005)