"1*2/1+2*3/1+3*4/1+.+2007*2008/1+2008*2009/1+2009*2010/1"这道题怎么做,

问题描述:

"1*2/1+2*3/1+3*4/1+.+2007*2008/1+2008*2009/1+2009*2010/1"这道题怎么做,

列项相消啊

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...(1/2007-1/2008)+(1/2008-1/2009)+(1/2009-1/2010)
=1-1/2010
=2009/2010