1/x(x+1)+……+1/(x+2011)(x+2012),其中1/x-1/x+2012=2012/x^2+2012x,且满足3x^2+6036x-2=0毫无头绪
问题描述：
1/x(x+1)+……+1/(x+2011)(x+2012),其中1/x-1/x+2012=2012/x^2+2012x,且满足3x^2+6036x-2=0
毫无头绪
答
前面的式子可以化简，后面没看懂你要问什么,难道是求值？
1/x(x+1)+……+1/(x+2011)(x+2012)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...........+1/(x+2011)-1/(x+2012)
=1/x-1/(x+2012)
=2012/（x^2+2012x）
=2012/(2/3)
=3*1006
=3018
答
1/x(x+1)+……+1/(x+2011)(x+2012)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+2011)-1/(x+2012)
=1/x-1/(x+2012)
=2012/(x²+2012x)
=6036/(3x²+6036x)
=6036/2
=3018