求和:1/2*1+1/2*3+1/3*4+…1/2009*2010

问题描述:

求和:1/2*1+1/2*3+1/3*4+…1/2009*2010

1/2*1+1/2*3+1/3*4+…1/2009*2010
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2009-1/2010)
=1-1/2010
=2009/2010