x x 1 1 x 1 x 2 1 x 2 x 31 x 2019 x 2019並且當x 1時,該

2022-12-24 23:41:02 字數 625 閱讀 7565

1樓:匿名使用者

解:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1(x+2009)(x+2010)

=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2009)-1/(x+2010)

=1/x-1/(x+2010)

故當x=1時,原式=1 -1/2011 =2010/2011

2樓:三味學堂答疑室

原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+2009)-1/(x+2010)

=1/x-1/(x+2010)

當x=1時,原式=1-1/2011=2010/2011

3樓:韻淵

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+2009)(x+2010)

=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+2009)-1/(x+2010)

=1/x-1/(x+2010)

=2010/x(x+2010)

當x=1時,原式=2010/2011

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