Question

数学极限题2道1,lim= [2^n+(a-1)^(n+1)] / [2^(n+1)+(a-1)^n] =1/2 ,则a

Answer 1

1.分子分母同除于2^n得

lim [2^n+(a-1)^(n+1)] / [2^(n+1)+(a-1)^n]

=lim {1+(a-1)[(a-1)/2]^n}÷{2+[(a-1)/2]^n}

=1/2

从而可知要求lim [(a-1)/2]^n=0,即要求 |(a-1)/2|