lim(n-->无穷）[(1+x)(1+x^2)(1+x^4)···(1+x^2n)]
=lim(n-->无穷)[(1-x)(1+x)(1+x^2)(1+x^4)...(1+x^2n)]/(1-x)
=lim(n-->无穷)(1-x^4n)/(1-x)
=1/(1-x)