计算x(x+1)/1+(x+1)(x+2)/1+(X+2)(x+3)/1+……+(x+2006)(x+2007)/1 ,并求x=1时,该代数式的值?

问题描述:

计算x(x+1)/1+(x+1)(x+2)/1+(X+2)(x+3)/1+……+(x+2006)(x+2007)/1 ,并求x=1时,该代数式的值?

1/x(x+1)+1/(x+1)(x+2)+1/(X+2)(x+3)+……+1/(x+2006)(x+2007)=1/x -1/(x+1)+1/(x+1) -1/(x+2)+1/(x+2) -1/(x+3)+……+1/(x+2006)-1/(x+2007)=1/x-1/(x+2007)=2007/x(x+2007)