1/2x5+1/5x8+1/8x11+.+1/2006x2009+2009x2013用裂项法计算
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1/2x5+1/5x8+1/8x11+.+1/2006x2009+2009x2013用裂项法计算
1/2x5+1/5x8+1/8x11+.+1/2006x2009+2009x2013用裂项法计算
1/2x5+1/5x8+1/8x11+.+1/2006x2009+2009x2013用裂项法计算
=1/3*(1/2-1/5)+1/3*(1/5-1/8)+.+1/3*(1/2006-1/2009)+1/3*(1/2009-1/2013)
=1/3*(1/2-1/5+1/5-1/8+.+1/2006-1/2009+1/2009-1/2013)
=1/3*(1/2-1/2013)
=1/3*1/2011
=1/6033
an = 1/[(3n-1)(3n+2)]
= (1/3)[ 1/(3n-1) - 1/(3n+2)]
Sn = a1+a2+...+an
= (1/3) [ 1/2 - 1/(3n+2) ]
1/(2x5)+1/(5x8)+1/(8x11)+...+1/(2006x2009)+1/(2009x2013)
= S670
= (1/3) ( 1/2 - 1/2012)
=335/2012
1/2x5+1/5x8+1/8x11+.+1/2006x2009+2009x2013用裂项法计算
裂项法1/2X5+1/5x8+1/8x11.1/2009x2012=?
1/2x5 +1/5x8 +1/8x11+……+1/2009x2012=?
1/2x5+1/5x8+1/8x11+1/11x14+1/14x17+1/17x20
2x5/1+5x8/1+8x11/1+.2006x2009/1+2009x2012/1 用裂项法计算
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1/5x8+1/8x11+1/11x14+.+1/98x101=1/(5x8)+1/(8x11)+1/(11x14)+.+1/(98x101)