Question

先观察下列等式,再回答问题．-1×1/2=-1+1/2,-1/2×1/3=-1/2+1/3,-1/3×1/4=-1/3+

Answer 1

(1)-(1/n)(1/(n+1))=-1/n+1/(n+1)

(2)

(-1×1/2)+(-1/2×1/2)+(-1/3×1/4)+…+(-1/2004×1/2005)

=-1+1/2+-1/2+1/3+-1/3+1/4+...+-1/2004+1/2005

中间项都是一正一负抵消

只剩头尾两项

=-1+1/2005

=-2004/2005