计算:1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2007)(x+2008).
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计算:1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2007)(x+2008).
计算:1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2007)(x+2008).
计算:1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2007)(x+2008).
原式可等价于1/X-1/(X+1)+1/(X+1)-1/(X+2)+.+1/(X+2007)-1/(X+2008)=1/X-1/(X+2008)=X/(X(X+2008))
原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+2007)-1/(x+2008)
=1/x)-1/(x+2008)
1/(X+1)(X+2)=1/(X+1)-1/(X+2)
1/(X+2)(X+3)=1/(X+2)-1/(X+3)
1/(X+2007)(X+2008)=1/(X+2007)-1/(X+2008)
所以原式
=1/(X+1)-1/(X+2)+1/(X+2)-1/(X+3)+……+1/(X+2007)-1/(X+2008)
=1/(X+1)-1/(X+2008)
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