lim(n→∞）（1+1/2)(1+1/4)(1+1/16)……(1+1/2^2^n）=lim(n→∞）(1-1/2)（1+1/2)(1+1/4)(1+1/16)……(1+1/2^2^n）/(1-1/2)=2lim(n→∞）(1-1/2)（1+1/2)(1+1/4)(1+1/16)……(1+1/2^2^n）=2lim(n→∞）[1-1/2^(2^n+1)]=2
