1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/10 12:05:09

1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)(x+2006) = 1/2x+4012

1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)(x+2006)
=1/(x+1)-1/(x+2) + 1/(x+2)-1/(x+3) + 1/(x+3)-1/(x+4) + .+ 1/(x+2005)-1/(x+2006)
=1/(x+1)-1/(x+2006)
=2005/(x+1)(x+2006)
1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)(x+2006) = 1/2x+4012
2005/(x+1)(x+2006) = 1/2x+4012
之后就是解方程了

x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4 x^5+x^4 = (x^3-x)(x^2+x+1)+x^2+x x^4+x^3+x^2+x+1=0,x^2006+x^2005+x^2004+x^2003+x^2002 |X-1|+|X-2|+|X-3|+|X-4|+|X-5|+|X-6|+|X-7|+|X-8|+|X-9|+|X-10| x-1)(X-2)(x-3)...(x-50)+x(x-2)(X-3)...(X-50)+...+x(x-1)(x-2) (x-1)^3(x+1)（x-2）/(x+4) （x+1)(x+2)(x+3)(x+4）+1 x(2-1/x)+x/(x^2-2x)÷(3-x)/(x^2-4) 1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...1/(x+2005)(x+2006) 1+x+x^2+x^3+.+x^99+x^100 （x+2/x+1）-（x+4/x+3）-（x+3/x+2）+（x+5/x+4）计算（x*x+4x+5）/（x+2）-（x*x+6x+10）/（x+3）+1