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已知m=2005,求m/(1x2)+m/(2x3)+m/(3x4)...+m/(2003x2004)+m/(2004x2

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/11/09 03:47:32
已知m=2005,求m/(1x2)+m/(2x3)+m/(3x4)...+m/(2003x2004)+m/(2004x2005)的值.
m/(1×2)+m/(2×3)+m/(3×4)+...+m/(2003×2004)+m/(2004×2005)
=m[1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2003×2004)+1/(2004×2005)]
=m(1-1/2+1/2-1/3+1/3-1/4+...+1/2003-1/2004+1/2004-1/2005)
=m(1-1/2005)
=2004m/2005
=2004×2005/2005
=2004