化简1/x(x+1)+1/(x+1)(x+2)+…+1/(x+2010)(x+2011),并求当x=1时该代数式的值.

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化简1/x(x+1)+1/(x+1)(x+2)+…+1/(x+2010)(x+2011),并求当x=1时该代数式的值.

化简1/x(x+1)+1/(x+1)(x+2)+…+1/(x+2010)(x+2011),并求当x=1时该代数式的值.
化简1/x(x+1)+1/(x+1)(x+2)+…+1/(x+2010)(x+2011),并求当x=1时该代数式的值.

化简1/x(x+1)+1/(x+1)(x+2)+…+1/(x+2010)(x+2011),并求当x=1时该代数式的值.

1/x(x+1)+1/(x+1)(x+2)+…+1/(x+2010)(x+2011),
=1/x-1/(x+1)+1/(x+1)-1/(x+1)+........+1/(x+2010)-1/(x+2011)
=1/x-1/(x+2011)
=2011/x(x+2011)
当x=1时
原式=2011/(1*(1+2011)
=2011/2012

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1/x(x+1)+1/(x+1)(x+2)+…+1/(x+2010)(x+2011)
=1/X-1/(x+1)+1/(x+1)1/(x+2)-1/(x+2)+......+1/(x+2010)-1/(x+2011)
=1/X-1/(x+2011)
当x=1时
原式=1/1-1/(1+2011)=1-1/2012=2011/2012