1\2*5+1\5*8+1\8*11.1\2009*2012+1\2012*2015裂项法解决,

1/(2*5)=(1/2-1/5)/3
1/(5*8)=(1/5-1/8)/3
所以原式=(1/2-1/5)/3+(1/5-1/8)/3+……+(1/2009-1/2012)/3+(1/2012-1/2015)/3=(1/2-1/5+1/5-1/8+……+1/2009-1/2012+1/2012-1/2015)/3=(1/2-1/2015)/3=671/4030