Question

Xn=(1+1/2^2)(1+1/2^2^2)……(1+1/2^2^n),则lim n趋向于∞时，Xn等于 A3/4 B4/3 C1 D∞

Answer 1

问：Xn=(1+1/2^2)(1+1/2^2^2)……(1+1/2^2^n),则lim n趋向于∞时，Xn等于 A3/4 B4/3 C1 D∞

答：A3/4

问：可以分析一下解题步骤吗，谢谢

答：(1-1/2^2)Xn=(1-1/2^2)(1+1/2^2)(1+1/2^4).….(1+1/2^(2^n))=(1-1/2^4)(1+1/2^4)..…(1+1/2^(2^n))=...=1-1/2^(2^(2n))令n->无穷，右端=1-0=1左端=(3/4)lim n->o Xn所以lim n->o Xn=4/3