1/1x3x5+1/3x5x7+1/5x7x9+......+1/2003x2005x2007

来源：百度知道编辑：UC知道时间：2024/07/04 20:09:53

分析:1/1x3x5=1/4×(1/1*3 -1/3*5)
1/3x5x7=1/4×(1/3*5 -1/5*7)
1/5x7x9=1/4×(1/5*7 - 1/7*9)
1/7*9*11=1/4×(1/7*9 -1/9*11)
.....................
1/2003x2005x2007=1/4×(1/2003*2005 -1/2005*207)
所有的等式相加有
1/1x3x5+1/3x5x7+1/5x7x9+.....+1/2003x2005x2007
=1/4×(1/1*3 -1/3*5 +1/3*5 -1/5*7+....+1/2003*2005-1/2005*2007)
=1/4×(1/1*3 - 1/2005*2007)
=335336/4024035
结论:1/n(n+1)(n+2)=1/2×[1/n(n+1) - 1/(n+1)(n+2)]
1/n(n+2)(n+4)=1/4×[1/n(n+2) - 1/(n+2)(n+4)]

1/1x3x5+1/3x5x7+1/5x7x9+......+1/2003x2005x2007 1/1x3x5+1/3x5x7+1/5x7x9+.....+1/2003x2005x2007=? (1x2x3+2x4x6+7x14x21)／(1x3x5+2x6x10+7x21x35) (1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) (1-1/100)(1-1/99)(1-1/98)......(1-1/3 1/( )+1/( )+1/( )+1/( )+1/( )+1/( )=1 (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000) (1/2003-1)(1/2002-1)(1/2001-1)...*(1/1001-1)(1/1000-1) (1-1/4)(1-1/9)(1-1/16)^(1-1/4008004)(1-1/4012009) 1+1/2+1+1/3+1+1/4+......+1/100=?