1/2*5+1/5*8+1/8*11+.+1/2006*2009+1/2009*2012

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1/2*5+1/5*8+1/8*11+.+1/2006*2009+1/2009*20121/2*5+1/5*8+1/8*11+.+1/2006*2009+1/2009*20121/2*5+1/5*8+

1/2*5+1/5*8+1/8*11+.+1/2006*2009+1/2009*2012
1/2*5+1/5*8+1/8*11+.+1/2006*2009+1/2009*2012

1/2*5+1/5*8+1/8*11+.+1/2006*2009+1/2009*2012
1/2*5+1/5*8+1/8*11+.+1/2006*2009+1/2009*2012
=(1/3)*(1/2-1/5+1/5-1/8+1/8-1/11+1/2009-1/2012)
=(1/3)*(1/2-2012)
=1/3*1005/2012
=335/2012

1/3((1/2-1/5)+(1/5-1/8)+ (1/2009-1/2012))
=1/3(1/2-1/2012)=335/2012