计算：1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+……+1/(x-2010)(x-2011)

来源：学生作业帮助网编辑：六六作业网时间：2024/12/29 12:51:26

计算：1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+……+1/(x-2010)(x-2011)计算：1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(

计算：1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+……+1/(x-2010)(x-2011)
计算：1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+……+1/(x-2010)(x-2011)

计算：1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+……+1/(x-2010)(x-2011)
1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+……+1/(x-2010)(x-2011)
=1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+1/(x-4)-1/(x-3)+.+1/(x-2011)-1/(x-2010)
=1/(x-2011)-1/(x-1)
=2010/[(x-2011)(x-1)]

原式=1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+1/(x-4)-1/(x-3).....+1/(x-2011)-1/(x-2010)
=1/(x-2011)-1/(x-1)

2010/[(x-2011)(x-1)]

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