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计算 1/(x+1)(x+2) + 1/(x+2)(x+3) +……+ 1/(x+2010)(x+2011)

来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/24 09:22:14
计算 1/(x+1)(x+2) + 1/(x+2)(x+3) +……+ 1/(x+2010)(x+2011)
计算 1/(x+1)(x+2) + 1/(x+2)(x+3) +……+ 1/(x+2010)(x+2011)
解: 1/(x+1)(x+2) + 1/(x+2)(x+3) +……+ 1/(x+2010)(x+2011)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+2010)-1/(x+2011)
=1/(x+1)-1/(x+2011)
=(x+2011-x-1)/[(x+1)(x+2011)]
=2010/[(x+1)(x+2011)]
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