1+1/2+1/4+1/8+1/16+.+1/512

1+1/2+1/4+1/8+1/16+.+1/512
1+1/2+1/4+1/8+1/16+.+1/512

1+1/2+1/4+1/8+1/16+.+1/512
等比数列 A(n+1)/An=q (n∈N*) 通项公式 An=A1*q^(n-1)
求和公式 Sn=A1(1-q^n)/(1-q) =(q≠1)
原式＝1*(1-(1/2)^10)/(1-1/2)=1023/512

= (1 - 1/512 * 1/2)/(1-1/2)
= 2 - 1/512
= 1025/512