设等比数列{q^(n-1)}(q>0)的前n项为Sn,A={x|x=limS(n+2)/Sn},求A
问题描述:
设等比数列{q^(n-1)}(q>0)的前n项为Sn,A={x|x=limS(n+2)/Sn},求A
答
等比数列Sn=(1-q^n)/(1-q),S(n+2)=(1-q^(n+2))/(1-q)
x=limS(n+2)/Sn=lim[(1-q^(n+2))/(1-q^n)] (n->+∞)
当0