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+.+1/1024
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+.+1/1024
很高兴回答你的问题
这道题是有技巧的,不是靠死算的
下面我给你算一下,希望你能学到其中的技巧1/2+1/4+1/8+1/16+1/32+1/64+1/128+.+1/1024
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+.+(1/64-1/128)+.+(1/512-1/1024)
=1-1/2+1/2-1/4+1/4-1/8+.+1/512-1/1024)=1-1/1024
=1023/1024

1023/1024

这是等比数列 q=1/2
1024=(1/2)^10
n=10
s=1/2(1-(1/2)^10)/(1-1/2)=1-(1/2)^10=1023/1024

S(n)=1/2(1-1/2^10)/(1-1/2)
=1023/1024

1/2+1/4+1/8+1/16+1/32+1/64+1/128+......+1/1024
=1-1/2+1/4+1/8+1/16+1/32+1/64+1/128+......+1/1024
=1-1/4+1/8+1/16+1/32+1/64+1/128+......+1/1024
=1-1/8+1/16+1/32+1/64+1/128+......+1/1024
=...
....
=1-1/1024
=1023/1024