1/(1×2)+1/(2×3)+1/(3×4)+...+1/[n(n+1)]>1949/1998
1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)>1949/1998
1- 1/(n+1)>1949/1998
n/(n+1)>1949/1998
1949(n+1)1949
n>1949/49,又n为正整数,n≥40
n的最小值为40.
以上为完整过程.