一道紧急数学题!1/2+1/6+1/12...+1/2008*2009=?

Question

一道紧急数学题!
1/2+1/6+1/12...+1/2008*2009=?

Answer 1

=1/1*2+1/2*3+1/3*4+……+1/2008*2009
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2008-1/2009)
中间正负抵消
=1-1/2009
=2008/2009