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?

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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?计算x(x+1)/1+(x+1)(x+2)/1+(X+

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?
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?

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)