Question

求解一道初中奥赛数学题!1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+.+1/2011-1/2012＝?求

Answer 1

1-1/2+1/3-1/4+.+1/2011-1/2012

=(1+1/3+1/5+.+1/2011)-(1/2+1/4+.+1/2012)

=(1+1/3+1/5+.+1/2011+1/2+1/4+.+1/2012)-(1/2+1/2+1/4+1/4+.+1/2012+1/2012)

=(1+1/2+1/3+1/4+.+1/2011+1/2012)-(1+1/2+1/3+.+1/1006)

=1/1007+1/1008+1/1009+.+1/2011+1/2012

我找不到更好的结果了