已知数列{an}满足:a1=2,an+1=3an+3的n+1次方-2的n次方(n∈N+)设Cn=an+1/an(n∈N+),是否存_数学解答

已知数列{an}满足:a1=2,an+1=3an+3的n+1次方-2的n次方(n∈N+)
设Cn=an+1/an(n∈N+),是否存在k∈N+,使得Cn≤Ck对一切正整数n均成立,并说明理由

人气：396 ℃　时间：2020-04-26 23:29:04

解答

a(n+1)=3an+3^(n+1)-2^na(n+1)/3^(n+1) - an/3^n = -(1/3)(2/3)^nan/3^n - a(n-1)/3^(n-1) = -(1/3)(2/3)^(n-1)an/3^n - a1/3 = -[ 1-(2/3)^n]an/3^n = -1/3+ (2/3)^nan = 2^n - 3^(n-1)cn = an + 1/anletf(x) = 2^x...