数列{an}满足:a1=2,an=[4a(n-1)]^5,求{an}的通项_数学解答

数列{an}满足:a1=2,an=[4a(n-1)]^5,求{an}的通项

人气：266 ℃　时间：2020-06-07 23:09:17

解答

a(n+1)=[4a(n)]^5,a(1)=2>0,a(n)>0.ln[a(n+1)]=5ln[4a(n)] = 5ln[a(n)] + 5ln(4),ln[a(n+1)] + x = 5ln[a(n)] + 5ln(4) + x = 5{ln[a(n) + ln(4) + x/5} = 5{ln[a(n)] + x},ln(4) + x/5 = x,x = (5/4)ln(4),ln[a(n+1...