x(x+1)分之1+（x+1)(x+2)分之1+(x+2)(x+3)分之1+.+（x+2010)(x+2011)分之1 x=1
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x(x+1)分之1+（x+1)(x+2)分之1+(x+2)(x+3)分之1+.+（x+2010)(x+2011)分之1 x=1
x(x+1)分之1+（x+1)(x+2)分之1+(x+2)(x+3)分之1+.+（x+2010)(x+2011)分之1 x=1
x(x+1)分之1+（x+1)(x+2)分之1+(x+2)(x+3)分之1+.+（x+2010)(x+2011)分之1 x=1
1/1*2+1/2*3+1/3*4+.+1/2011*2012
1-1/2+1/2-1/3+1/3-1/4+.+1/2011-1/2012
=1-1/2012
=2011/2012
1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+2010)-1/(x+2011)
=1-1/2012
=2011/2012
x(x+1)分之1=x分之1-(x+1)分之1.....你利用这个公司在计算下。。
原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+2010)-1/(x+2011)
=1/x-1/(x+2011)
=2011/x(x+2011)
=2011/2002
x(x+1)分之1+（x+1)(x+2)分之1+(x+2)(x+3)分之1+....+（x+2010)(x+2011)分之1
=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+...+[1/(x+2010)-1/(x+2011)]
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2010)-1/(x+2011)
=1/x-1/(x+2011)
∵x=1
1/x-1/(x+2011)=1-1/2012=2011/2012
题目意思不是很清楚额。。
x(x+1)分之1+（x+1)(x+2)分之1+(x+2)(x+3)分之1+....+（x+2010)(x+2011)分之1的计算是：
1/x(x+1)+1/（x+1)(x+2)+1/(x+2)(x+3)+....+1/（x+2010)(x+2011)=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+2010)-1/(x+2011)=1/x-1/(x+2011)
原式=1/(1*2)+1/(2*3)+1/(3*4)+……+1/(2011*2012)=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012=2011/2012
x(x+1)分之1+（x+1)(x+2)分之1+(x+2)(x+3)分之1+....+（x+2010)(x+2011)分之1
x(x+1)分之1=1/x - 1/(x+1)
同理（x+1)(x+2)分之1 = 1/(x+1) - 1/(x+2)
以此类推
（x+2010)(x+2011)分之1 = 1/(x+2010) - 1/(x+2011)
代入原式后，原式=1/x - 1/（x+2011）
因为x=1.所以原式=2011/2012
原式=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+...+[1/(x+2010)-1/(x+2011)]
=1/x-1/(x+2011)
代入x=1
=2011/2012