1/(2*5)+1/(5*8)+1/(8*11)+.+1/(2006*2009)+1/(2009*2012)怎么做?

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1/(2*5)+1/(5*8)+1/(8*11)+.+1/(2006*2009)+1/(2009*2012)怎么做?1/(2*5)+1/(5*8)+1/(8*11)+.+1/(2006*2009)+1

1/(2*5)+1/(5*8)+1/(8*11)+.+1/(2006*2009)+1/(2009*2012)怎么做?
1/(2*5)+1/(5*8)+1/(8*11)+.+1/(2006*2009)+1/(2009*2012)怎么做?

1/(2*5)+1/(5*8)+1/(8*11)+.+1/(2006*2009)+1/(2009*2012)怎么做?
原式=1/3(1/2-1/5+1/5-1/8+...+1/2009-1/2012)
= 1/3(1/2-1/2012)
=335/2012

=(3/(2*5)+3/(5*8)+3/(8*11)+......+3/(2006*2009)+3/(2009*2012))/3
=(1/2-1/5+1/5-1/8+1/8-1/11+...+1/2006-1/2009+1/2009-1/2012)/3
=(1/2-1/2012)/3
=(1006-1)/2012/3
=335/2012