Question

(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1

Answer 1

首先把负号提出来,则有

1x1/2=1-1/2

1/2x1/3=1/2-1/3

1/3x1/4=1/3-1/4

.

1/2008X1/2009=1/2008-1/2009

将以上各式相加,得原式=-（1-1/2009）=-2008/2009