请问个数学问题

求1/2+1/2²+1

S=1/2+1/4+1/8+1/16+……+1/2^n。 用小学四年级的方法： S+1/2^n =[1/2+1/4+1/8+1/16+……+1/2^(n-2)+1/2^(n-1)+1/2^n]+1/2^n =1/2+1/4+1/8+1/16+……+1/2^(n-2)+1/2^(n-1)+[1/2^n+1/2^n] =1/2+1/4+1/8+1/16+……1/2^(n-2)+1/2^(n-1)+1/2^(n-1) =1/2+1/4+1/8+1/16+……1/2^(n-2)+[1/2^(n-1)+1/2^(n-1)] =1/2+1/4+1/8+1/16+……+1/2^(n-2)+1/2^(n-...全部

  S=1/2+1/4+1/8+1/16+……+1/2^n。 用小学四年级的方法： S+1/2^n =[1/2+1/4+1/8+1/16+……+1/2^(n-2)+1/2^(n-1)+1/2^n]+1/2^n =1/2+1/4+1/8+1/16+……+1/2^(n-2)+1/2^(n-1)+[1/2^n+1/2^n] =1/2+1/4+1/8+1/16+……1/2^(n-2)+1/2^(n-1)+1/2^(n-1) =1/2+1/4+1/8+1/16+……1/2^(n-2)+[1/2^(n-1)+1/2^(n-1)] =1/2+1/4+1/8+1/16+……+1/2^(n-2)+1/2^(n-2) =…… =1/2+1/4+1/8+1/16+1/16 =1/2+1/4+1/8+1/8 =1/2+1/4+1/4 =1/2+1/2 =1。
   S=1-1/(2^n)。收起