An=[2^n-(1+q)^n]/(1-q) -3<q<1,且q不等于-1,求lim (An/2^n) 注：2^n为2的n次方
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解：∵-3<q<1,且q不等于-1
∴-3<q<-1或-1<q<1
==>-2<q+1<0或0<q<2
==>-1<(q+1)/2<0或0<(1+q)/2<1
==>lim(n->∞){[(q+1)/2]^n}=0
故lim(n->∞)(An/2^n)=lim(n->∞){[2^n-(1+q)^n]/[(1-q)2^n]}
=[1/(1-q)]*lim(n->∞){1-[(1+q)/2]^n}
=[1/(1-q)]*(1-0)
=1/(1-q)
∴-3<q<-1或-1<q<1
==>-2<q+1<0或0<q<2
==>-1<(q+1)/2<0或0<(1+q)/2<1
==>lim(n->∞){[(q+1)/2]^n}=0
故lim(n->∞)(An/2^n)=lim(n->∞){[2^n-(1+q)^n]/[(1-q)2^n]}
=[1/(1-q)]*lim(n->∞){1-[(1+q)/2]^n}
=[1/(1-q)]*(1-0)
=1/(1-q)
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