1/2+1/4+1/8+…+1/256+1/512+1/1024=?

1/2+1/4+1/8+…+1/256+1/512+1/1024=?
1/2+1/4+1/8+…+1/256+1/512+1/1024=?

1/2+1/4+1/8+…+1/256+1/512+1/1024=?
1/2=1-1/2
1/4=1/2-1/4
1/8=1/4-1/8
.
1/512=1/256-1/512
+1/1024=1/512-1/1024
_____________________
1/2+1/4+1/8+…+1/256+1/512+1/1024=1-1/1024= 1023/1024=0.9990234375

等比数列,根据公式
=1023/1024

等比数列求和，有公式的1/2+（1/2）^2+(1/2)^3+......+(1/2)^10=(1/2)(1-(1/2)^10)/(1-(1/2)=1023/1024

1023/1024