lim(1+1/2+.+1/2^n)
和
lim(1+1/4+.1/4^n)
都存在,所以
lim[(1+1/2+.+1/2^n)/(1+1/4+.1/4^n)]
=lim(1+1/2+.+1/2^n)/lim(1+1/4+.1/4^n)
lim(1+1/2+.+1/2^n)
=lim(1-1/2^n)/(1-1/2)=2
lim(1+1/4+.1/4^n)
=lim(1-1/4^n)/(1-1/4)=4/3
所以
lim[(1+1/2+.+1/2^n)/(1+1/4+.1/4^n)]
=2÷(4/3)
=3/2