hzbn.net
当前位置:首页>>关于(1-1/4)1-1/9括号1-1/16省略号括号1-1/百的资料>>

(1-1/4)1-1/9括号1-1/16省略号括号1-1/百

根据平方差公式, 原式 = (1-1/2)(1+1/2) * (1-1/3)(1+1/3) * (1-1/4)(1+1/4) *......*(1-1/100)(1+1/100) = 1/2*3/2*2/3*4/3*3/4*5/4*......*99/100*101/100 = 1/2*101/100 = 101/200

供参考。

(3/4-1/16)×(1/9+1/3)用递等式计算 =(12/16-1/16)x(1/9+3/9) =11/16x4/9 =11/36

1+1/4+1/9.+1/N^2 =1+1/2*2+1/3*3+...1/N*N <1+1/1*2+1/2*3.+1/(N-1)N =1+1-(1/2)+(1/2)-(1/3).-1/N =2-1/N 所以原式成立

=(1-1╱2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/1000)(1+1/1000)=1/2×3/2×2/3×4/3×3/4……999/1000×1001/1000=1001/2000

1+2*2+3*3+...+n*n=1+1*2+2+2*3+3+3*4+4+....(n-1)n+n =(1+2+3+...+n)+[1*2+2*3+3*4+....(n-1)*n] =n(n+1)/2+[1*2*3+2*3*3+3*4*3+....(n-1)*n*3]/3 =n(n+1)/2+[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+......(n-1)n(n+1)-(n-2)(n-1)n]/3 =n(n+1)/2+(n-1)...

原式 =(1-1/2)(1+1/2) * (1-1/3)(1+1/3) * ... * (1-1/10)(1+1/10) =1/2 * 2/3 * 3/4 * ... * 9/10 * 3/2 * 4/3 * 5/4 * ... * 11/10 整理,抵消 =1/2 * 11/10 =11/20

25, 36

(1-1/4)(1-1/9)(1-1/16)(1-1/25)(1-1/36)(1-1/49)(1-1/64)(1-1/81)(1-1/100) =(1-1/2)(1+1/2)(1-1/3)(1+1/3)``````(1-1/10)(1+1/10) =1/2*3/2*2/3*4/3``````*9/10*11/10 =11/20

派的平方除以6

网站首页 | 网站地图
All rights reserved Powered by www.hzbn.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com