1+1/4+1/16+1/64+1/256+1/10241/18+1/54+1/108+1/180+1/270+1/378+1/504+1/648+1/810+1/990

来源：学生作业帮助网编辑：作业帮时间：2024/05/13 04:20:47

1+1/4+1/16+1/64+1/256+1/10241/18+1/54+1/108+1/180+1/270+1/378+1/504+1/648+1/810+1/990
1+1/4+1/16+1/64+1/256+1/1024
1/18+1/54+1/108+1/180+1/270+1/378+1/504+1/648+1/810+1/990

1+1/4+1/16+1/64+1/256+1/10241/18+1/54+1/108+1/180+1/270+1/378+1/504+1/648+1/810+1/990
设S=1+1/4+1/16+1/64+1/256+1/1024-------------------①
则S/4= 1/4+1/16+1/64+1/256+1/1024+1/4096--------②
①-②=3S/4=1-1/4096=4095/4096
所以：S=4095/4096*4/3
=1365/1024
1/18+1/54+1/108+1/180+1/270+1/378+1/504+1/648+1/810+1/990
=1/(3*6)+1/(6*9)+1/(9*12)+.+1/(30*33)
=1/3*[(1/3-1/6)+(1/6-1/9)+(1/9-1/12)+.+(1/30-1/33)]
=1/3*(1/3-1/6+1/6-1/9+1/9-1/12+.+1/30-1/33)
=1/3*(1/3-1/33)
=(1/3)*(10/33)
=10/99
类似：1/[a*(a+n)]=(1/n)*[1/a-1/(a+n)]
例子：
1/56=1/(7*8)=1/7-1/8
1/12=1/(2*6)=(1/4)*[1/2-1/6]
.
等等
以上的式子是很重要的,能记住对解这类的题是有帮助的~

是在EXCEL中吗？2^1024超出了EXCEL能处理的数据范围，显示为错误值。如果是要简化公式，比如 =SUM(2 1,2^2 1,2^4 1,2^8 1,2^16 1,2^32 1

1365/1024
1.3330078

设S=1+1/4+1/16+1/64+1/256+1/1024-------------------①
则S/4= 1/4+1/16+1/64+1/256+1/1024+1/4096--------②
①-②=3S/4=1-1/4096=4095/4096
所以：S=4095/4096*4/3
=1365/1024

1,4,9,16,25,( ),( ),64,81 1,4,9,16,25?64,81 (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) (1-1/4)(1-1/9)(1-1/16)(1-1/25)(1-1/36)(1-1/49)(1-1/64)(1-1/81)(1-1/100) 找规侓 1,1,4,8,9,27,16,64,25,(),() 1,4,9,16,25,（）49,64,（）,（）, 1,9,16,25,64,81 计算行列式1,1,1,1;2,3,4,5;4,9,16,25;16,27,64,125计算行列式1,1,1,1;2,3,4,5;4,9,16,25;16,27,64,125 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 1/2-1/4-1/8-16/1-32/1-64/1-128/1-256/1 1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256 1/2+1/4+1/8+1/16+1/32+1/64+1/128+.+1/1024 1-2/1-4/1-8/1-16/1-32/1-64/1-128/1 1/2-1/4-1/-1/8-1/16-1/32-1/64----------1/1024 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 线性代数问题设D=1 1 1 1 2 3 4 5 4 9 16 25 16 27 64 125 求D的值1 1 1 12 3 4 54 9 16 25 16 27 64 125 (1-1/4)(1-1/9)(1-1/16)(1-1/25)...(1-1/10000) 速度(1-1/4)×（1-1/9)×(1-1/16)×(1-1/25)×.×(1-1/10000)