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
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