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

来源：学生作业帮助网编辑：作业帮时间：2024/04/28 09:14:03

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

(x-2分之x-1)/2-x分之4x x-1分之x²+5x - x²-x分之2x²+4x X(X-1)分之2X+1 (x-1分之2x-x+1分之3x)除以x^2-1分之x (x-1分之2x - x+1分之x)×x分之x²-1= (x平方-2x分之x+2-x平方-4x+4分之x-1)乘4-x分之x (x-2x分之x+2 - x-4x+4分之x-1)/x分之x-4 (x-(x+1分之2x))除以x^2-1分之x^2-2x+1 [x-(x+1分之2x)]÷x²-1分之x²-2x+1 x^2-x+3分之1-2x,-x^2+x-3分之2x-1 x方-2x+1分之x方-1+x-2分之x方-2x x²-2x分之x+2-x²-4x+4分之x-1 先化简再求值 x-1分之4(x-x)+(x-2) 2x分之1- x+y分之1(2x分之x+y -x-y)化简 1-x平方-4分之4x=x+2分之x+x-2分之2 x的平方-9分之2x+3-x分之1+x+3分之x+2 （x-2分之3x-x+2分之1）乘x分之x平方-4 x²+x分之2+x²-x分之3=x平方-1分之4