1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),

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1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),
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1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),
答：
原式
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+1998)-1/(x+1999)
=1/x-1/(x+1999)
=1999/[x(x+1999)]

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+......+1/(x+1998)(x+1999),当x=1
2000/1999

1/x-1/(x+1999)

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