limn趋向于无穷2的n幂+3的n次幂除以2的n+1次幂+3的n+1次幂怎么求啊

Question

lim n趋向于无穷 2的n幂+3的n次幂除以2的n+1次幂+3的n+1次幂 怎么求啊

Answer 1

原式=lim n趋向于无穷（2^n+3^n)/[2^(n+1)+3^(n+1)]
=lim n趋向于无穷（2^n+3^n)/[3(2^n+3^n)-2^n]
=lim n趋向于无穷1/[3-2^n/（2^n+3^n)]
=lim n趋向于无穷1/[3-1/[1+(3/2)^n]]
=1/(3-0)
=1/3