1/2x5+1/5x8+1/8x11+.+1/2006x2009+2009x2013用裂项法计算

TY原是这样黑2022-10-04 11:39:542条回答

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mycheng 共回答了17个问题 | 采纳率76.5%: =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; 1年前

cvoiadsfupoausdo 共回答了1627个问题 | 采纳率: 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年前

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1/2x5+1/5x8+1/8x11+…………+1/2003x2006+1/2006x2009 = 这是我儿子的小学作业 1/2x5+1/5x8+1/8x11+…………+1/2003x2006+1/2006x2009 = 这是我儿子的小学作业,我想不出简便算法…… 趴趴恋井1年前3: 下午茶_a 共回答了15个问题 | 采纳率86.7%

1/2x5+1/5x8+1/8x11+…………+1/2003x2006+1/2006x2009
=1/3x(3/2x5+3/5x8+.+3/2006x2009)
=1/3x(1/2-1/5+1/5-1/8+...+1/2006-1/2009)
=1/3x(1/2-1/2009)
=1/3x2007/2009
=669/2009

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