www.whkt.net > 求文档: 1x3x5+3x5x7+5x7x9+7x9x11,求巧算

求文档: 1x3x5+3x5x7+5x7x9+7x9x11,求巧算

规律(2*X-13)*(2*X-11)*(2*X-9)X=1,2,3,4,5,6,7,8,9,10,11,12答案是:(-11)*(-9)*(-7),(-9)*(-7)*(-5),(-7)*(-5)*(-3),(-5)*(-3)*(-1),(-3)*(-1)*1,(-1)*1*3

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+..+1/2003x

用一个一般关系:1/n(n+2)(n+4)=1/8[1/n-2/(n+2)+1/(n+4)]也就是说:1/1x3x5=1/8[1/1-2/3+1/5]1/3x5x7=1/8[1/3-2/5+1/7]……1/95x97x99=1/8[1/95-2/97+1/99]相加的时候,写成竖式更容易看出来结果为=1/8[1-1/3-1/97+1/99]

1/1x3x5+1/3x5x7+1/5x7x9+…+1/95x97x99=1/4(1/(1*3)-1/(3*5)+1/(3*5)-1/(5*7)+..+1/(95*97)-1/(97*99)= (1/4) ( 1/(1x3) - 1/(97x99)= (1/4) (1/3 - 1/9603]=800/9603

2006+200.6+20.06+2.006= 2.006 * 1000 + 2.006 * 100 + 2.006 * 10 + 2.006= 2.006 * (1000 + 100 + 10 + 1)= 2.006 * 1111= 2228.666

=1/4*(1/1*3-1/3*5)+1/4*(1/3*5-1/5*7)+1/4*(1/5*7-1/7*9)+……+1/4*(1/17*19-1/19*21)=1/4*(1/1*3-1/19*21)=11/133

3.412+2.565.89+0.918=(3.412+0.918)+(2.565.89)=4.33-3.33=1 应该是这样的比较好: 3.412+2.565.89+0.918=(3.412+0.918)-(5.89-2.56)=4.33-3.33=1

=1*2*3(1+3^3+5^3+7^3)/1*3*5(1+3^3+5^3+7^3)=2/5.希望可以帮到你,(*^__^*)

0.4444+22.22*222.22+1777.6*22.222=0.4444

相关搜索:

网站地图

All rights reserved Powered by www.whkt.net

copyright ©right 2010-2021。
www.whkt.net内容来自网络,如有侵犯请联系客服。zhit325@qq.com