计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……1/(x+1998)(x+1999)
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计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……1/(x+1998)(x+1999)计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……1/(x
计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……1/(x+1998)(x+1999)
计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……1/(x+1998)(x+1999)
计算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+1) 同理1/（x+n)(x+n+1)=1/(x+n)-1/(x+n+1) 所以上公式=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-1/(x+1)+1/(x+1)-1/(x+2) 同理 所以，上式等于=1/x-1/(x+1999)=1999/x(x+1999)
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