1+1/4+1/16+1/64+1/256+1/1024

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/12 15:59:16

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

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~

1-1/2+1/4-1/8+1/16-1/32+1/64-1/128+1/256-1/512+1/1024-1/2048 速算与巧算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024+1/4 1+1+2+4+8+16+32+64+128+256+512+1024+2048+4096=? 计算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024 要解题思路, 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024 讲的好懂点 2/1+4/1+8/1+16/1+32/1+64/1+128/1+256/1+512/1+1024/1=? 1024+512+256+128+64+32+16+8+4+2+1等于多少?要简便运算! 1024+512+256+128+64+32+16+8+4+2+1求解 1+2+4+8+16+32+64+128+256+512+1024+2048+4096+8192+16384+32768 1+2+4+8+16+32+64+128+256+512+1024+2048+4096+8192+.+99999 1+2+4+8+16+32+64+128+256+512+1024=______．