已知数列{an}中,a1=1,an+1=100an²,求通项an
问题描述:
已知数列{an}中,a1=1,an+1=100an²,求通项an
答
1ogan+1=log100+2logan,即1ogan+1=2logan+2,即[(1ogan+1)+2]=2(logan+2),数列logan+2是以公比为2的等比数列.logan+2=2^(n-1)(1oga1+2)=2^n,logan=2^n-2,an=10^(2^n-2).