1除以(X+1)X+2)+1除以(X+3)(X+4)...1除以(X+2005)(X+2006)等于几

1除以(X+1)X+2)+1除以(X+3)(X+4)...1除以(X+2005)(X+2006)等于几?
是1除以(X+1)X+2)+1除以(X+3)(X+4)...1除以(X+2005)(X+2006)等几 不是1除以(X+1)X+2)+1除以(X+2)(X+3)...1除以(X+2005)(X+2006)等于几

裂项相消。1/(x+a)(x+b)=【1/(x+a)-1/(x+b)】*1/(b-a)
一般都是这种形式。特别是你那道题的形式应该让你联想起来这种形式。
比如1/(x+1)(x+3)+1/(x+3)(x+5)=1/2*[1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)]
要融会贯通,不要拘泥于一道题的答案,这样的题就都会了。
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第1个回答  2007-11-04
1除以(X+1)-1除以(X+2006)
可以分解为1/(X+1)-1/(X+2)+1/(X+2)-1/(X+3)`````+1/(X+2005)-1/(X+2006)
第2个回答  2007-11-08
NO

1除以(X+1)X+2)+1除以(X+3)(X+4)...1除以(X+2005)(X+2006)等于几
比如1\/(x+1)(x+3)+1\/(x+3)(x+5)=1\/2*[1\/(x+1)-1\/(x+3)+1\/(x+3)-1\/(x+5)]要融会贯通,不要拘泥于一道题的答案,这样的题就都会了。

如何化简下列算式1\/x + 1\/x(x+1) + 1\/(x+1)(x+2)+...+1\/(x+20
1\/x+1\/x(x+1)+1\/(x+1)(x+2)+...+1\/(x+2004)(x+2005)=1\/x + 1\/x -1\/(x+1)+1\/(x+1)-1\/(x+2)+...+1\/(x+2004)-1\/(x+2005)=1\/x+1\/x-1\/(x+2005)= [2(x+2005)-x]\/[ x(x+2005)]=(x+4010)\/[ x(x+2005)]同理 1\/x(x+2) =1\/2 [1\/X-1\/...

解分式方程1\/x(x+2)+1\/(x+2)(x+4)+1\/(x+4)(x+6)=3\/2(x+6)
2\/x=(3x+10)\/2(x+6)3x²+10x=4x+24 3x²+6x-24=0 x²+2x-8=0 (x+4)(x-2)=0 ∴x=-4 x=2 检验:x=-4是增根 ∴方程的解是x=2

求1\/(1x2)+1\/(2x3)+1\/(3x4)+1\/(4x5)+...+1\/(2005x2006)
除了最左边和最右边的一项其余通通可以抵消即原式等于1减2006分之1等于2OO6分之2005 我是数学老师不懂再来问我好了.

1\/(x*(x+1)*(x+2)) 怎么因式分解
1 = A(x + 1)(x + 2) + Bx(x + 2) + Cx(x + 1)代入x = 0 1 = 2A ==> A = 1\/2 代入x = - 1 1 = - B ==> B = - 1 代入x = - 2 1 = C(- 2)(- 1) ==> C = 1\/2 所以1\/[x(x + 1)(x + 2)] = 1\/(2x) - 1\/(x + 1) + 1\/[2(x ...

x(x+1)(x+2)(x+3)+1分解因式
(x+1)(x+2)(x+3)(x+4)+1 =(x+1)(x+4)(x+2)(x+3)+1 =(x^+5x+4)(x^+5x+6)+1 另x^+5x=y,则原式变为 (y+4)(y+6)+1 =y^+10y+25 =(y+5)^ 把x^+5x=y代入,得(x^+5x+5)^ 参考资料:仅供参考,祝你学习进步!

(x+1)(x+2)(x+3)(x+4)+1怎么因式分解?
(x+1)(x+2)(x+3)(x+4)+1 =[(x+1)(x+4)][(x+3)(x+2)]+1 =(x^2+5x+4)(x^2+5x+6)+1 把(x^2+5x)看做一个整体 =(x^2+5x)^2+10(x^2+5x)+24+1 =(x^2+5x)^2+10(x^2+5x)+25 完全平方公式 =(x^2+5x+5)^2 因式分解:因式分解是中学数学中最重要的...

X除以1*2+x除以2*3+x除以3*4+...+x除以2005*2006等于2005,这个方程的解...
原方程可化为:x(1\/1×2+1\/2×3+1\/3×4+ ...+1\/2005×2006)= 2005 这里面需要用到小学奥数的裂项相消:x(1-1\/2+1\/2-1\/3+ ...-1\/2005+1\/2005-1\/2006)=2005 x×(1-1\/2006)=2005 x×2005\/2006=2005 x = 2006

y=x(x+1)(x+2)(x+3)...(x+n)的导数求法,(详细)
x+n)]'所以,(1\/y)*y'=1\/x+1\/(x+1)+1\/(x+2)+1\/(x+3)+---1\/(x+n)所以,y'=y[1\/x+1\/(x+1)+1\/(x+2)+1\/(x+3)+---1\/(x+n)]即:y'=[x(x+1)(x+2)(x+3)---(x+n)][1\/x+1\/(x+1)+1\/(x+2)+1\/(x+3)+---1\/(x+n)]...

6、幂级数f(x)=1\/(x^2+3x+2)展开成(x+4)的形式.
f(x)=1\/[(x+1)(x+2)]=1\/(x+1)-1\/(x+2)=1\/(x+4-3)-1\/(x+4-2)=(-1\/3)\/[1-(x+4)\/3]+(1\/2)\/[1-(x+4)\/2]=(1\/2)∑[(x+4)\/2]^n-(1\/3)∑[(x+4)\/3]^n=∑[1\/2^(n+1)-1\/3^(n+1)](x+4)^n.收敛域 -1 ...

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