1/1x3x5+1/3x5x7+1/5x7x9+.....+1/2003x2005x2007=?
来源:百度知道 编辑:UC知道 时间:2024/09/22 16:09:07
今天就要,过程也要,奖分多多
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=?