本x2 (X-1)+(X-2)+(X-3)+.+3+2+1的值为多少，为什么书上是1/2X(X-1)?

(X-1)+(X-2)+(X-3)+.+3+2+1的值为多少，为什么书上是1/2X(X-1)?  

(X-1)+(X-2)+(X-3)+...+3+2+1的值为多少，为什么书上是1/2X(X-1)?

解：
设值为s，考虑到从两头取数相加好都为X，则不妨都相加，即
s=(X-1)+(X-2)+(X-3)+...+3+2+1
s=1+2+3+……+(X-3)+(X-2)+(X-1)
两式相加得
2s=X+X+X+……+X+X+X=X(X-1) （一个有X-1个）
s=1/2X(X-1)

书上没错

化简求值1/(x-1) +1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4),x为104

答案是0.01,1=（x-1)-(x-2)=(x-2)-(x-3).....约去分子即可

|x-1|+|x-2|+|x-3|+........+|x-2011|最小值为多少?

x=1006最小，1006*1005 ,相当于在实数轴上找一点到1,2...2011距离的和最小显然[1,2011]的中点满足条件，你可以用反证法证明

计算:1/(x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2)

1/(x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2)
=(x-1)/(x-2)(x-3)(x-1)-2(x-2)/(x-1)(x-2)(x-3)+(x-3)/(x-1)(x-2)(x-3)
=【x-1-2x＋4＋x-3】/(x-1)(x-2)(x-3)
=【0】/(x-1)(x-2)(x-3)
=0

若x=-0.279,则|x-1|+|x-3|+....+|x-2001|-|x|-|x-2|-....-|x-2000|值为多少

∵x=-0.279
∴|x-1|=1-x
|x-3|=3-x
.................
|x-2001|=2010-x
|x|=-x
|x-2|=2-x
........................
|x-2000|=2000-x

∴|x-1|+|x-3|+....+|x-2001|-|x|-|x-2|-....-|x-2000|
=（1-x)+(3-x)+.......+(2001-x)-(-x)-(2-x)-(4-x)-......-(2000-x)
=(1-0)+(3-2)+(5-4)+.....+(2001-2000)+(x-x)+.....(x-x)
=1000

1/x(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)化简

1/x(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)
=1/x(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)
=1/(x-1)-1/x+1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)
=1/(x-3)-1/x
=3/[x(x-3)]

已知x^2-5x-2000=0则(x-2)^3-(x-1)^2+1/x-2的值为多少，要过程

这一题怎么算出来这么烦：
设x-2=t 则(t+2)^2-5*(t+2)-2000=0
则 t^2-t=2006
原式：t^3-(t+1)^2+1/(t+2)-2
=t^3-t^2-2t+1/(t+2)-3
=t(t^2-t)-2t+1/(t+2)-3
=2004t+1/(t+2)-3
然后就是把t求出来了，再带进去
（我水平有限，只能算到这样了，见谅）

观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2);

可以归纳出一般的结论是：相邻的两个自然数积的倒数等于这两个自然数的倒数之差！

1/(x-1)(x-2)+1/(x-2)(x-3)+……+1/(x-99)(x-100)
=1/(x-1)-1/(x-2)+1/(x-2)-1/(x-3)+……+1/(x-99)-1/(x-100)
=1/(x-1)-1/(x-100)
=[(x-100)-(x-1)]/[(x-1)(x-100)]
=-99/[(x-1)(x-100)]

求：2X^3+X^2-X-2=A(X-1)(X-2)(X-3)+BX(X-2)(X-3)+CX(X-1)(X-3)+DX(X-1)(X-2),求实数A,B,C,D的值

1，2，46，89

1/(x-2)(x-3)-3/(x-1)(x-4)+1/(x-1)(x-2)=1/(x-4)

去分母：(x-1)(x-4)-3(x-2)(x-3)+(x-3)(x-4)=(x-1)(x-2)(x-3)
整理，得：x³-5x²+8x-4=0
解得：x=1或x=2
x=1或x=2时：(x-1)(x-2)(x-3)(x-4)=0
原方程无解。