来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/02 15:57:50
一道简单的数学趣味计算题
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+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)
=2005/a(a+2005)