Question

1/1X2+1/2X3+1/3X4+……+1/nX(n+1)>1949/1998.n最小是几

Answer 1

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.