ppts.net
当前位置:首页>>关于(1-3/2*4)*(3/3*5)*(1-3/4*6)*......*(1-3/7*9)的资料>>

(1-3/2*4)*(3/3*5)*(1-3/4*6)*......*(1-3/7*9)

观察:2*4,3*5……,整个式子中只有它在变,设它为(n-1)*(n+1),因为这样的话,第一项取3,第二项取4…… 通分:得到每一项的通式(n^2-1-3)/(n^2-1)=(n+2)(n-2)/(n+1)(n-1) 【3

把分子写成分母的最大数减1 ,得 原式=(2-1)/(1*2)+(3-1)/(1*2*3)+(4-1)/(1*2*3*4)+(5-1)/(1*2*3*4*5) =[2/(1*2)-1/(1*2)]+[3/(1*2*3)-1/(1*2*3)]+[4/(1*2*3*4)-1/(1*2*3*4)]+[5/(1*2*3*4*5)-1/(1*2*3*4*5)] =[1/1-1/(1*2)]+[1/(1*2)-1/(1*2*3)]...

从8个分数的特点可以写出 (n+3)/n*(n+1)*(n+2)=x/n*(n+1)-y/(n+1)*(n+2), 对右边通分 [x(n+2)-ny]=n*(n+1)*(n+2)=(n+3)/n*(n+1)*(n+2) 两边的分子相等 (x-y)n+2x=n+3 两边的同类项系数对应相等x-y=1, 2x=3, 解得x=3/2, y=1/2 原式=1/2{[3/1*2-1/...

你把括号去掉,每个括号的最后一个和后一个括号的第一个相乘为1,然后就整理为1/2乘2015/2014等于2015/4028

1/(1×3)=½(1-1/3), 1/(2×4)=½(1/2-1/4), 1/(3×5)=½(1/3-1/5), …… 1/[n×(n+2)]=½[1/n-1/(n+2)], …… 1/(48×50)=½(1/48-1/50), 原式=½[1-1/3+1/2-1/4+1/3-1/5+…+1/n-1/(n+2)+…+1/46-1/48+1/47-1/49+1/48-1/50] ...

上式=(2*2/1*3)*(3*3/2*4)*(4*4/3*5)*(5*5/4*6)...*(10*10/9*11) =(2^2*3^2*4^2*...*10^2)/(1*2*3^2*4^2*...*9^2*10*11) =(2^2*10^2)/(1*2*10*11)=20/11

解: 4/5/(3/5+1/2)*2 =4/5/(6/10+5/10)*2 =4/5/(11/10)*2 =4/5*10/11*2 =40/55*2 =80/55 =16/11

解法一: 1×2+2×3+3×4+...+n(n+1) =⅓×[1×2×3-0×1×2+2×3×4-1×2×3+3×4×5-2×3×4+...+n(n+1)(n+2)-(n-1)n(n+1)] =⅓n(n+1)(n+2) 解法二: 考察一般项第k项,k(k+1)=k²+k 1×2+2×3+3×4+...+n(n+1) =(1²+2²+3²+...+n...

1/(2*3)+1/(3*4)+1/(4*5)+......+1/(99*100) =1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100 =1/2-1/100 =49/100 =0.49

=1009/2019

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