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
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
原式=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+2010) - 1/(x+2011)
=1/x - 1/(x+2011)
当x=1时
原式=1- 1/2012
=2011/2012
=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)
=2011/2012
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