已知a1=1,an+1=an²-2an+2.①证:{log2(a-1)}为等比数列.②求an
问题描述:
已知a1=1,an+1=an²-2an+2.①证:{log2(a-1)}为等比数列.②求an
n+1为右下角角码
答
an+1 -1=(an-1)²
log2(an-1)=log2(an-1 -1)²
=2log2(an-1 -1)
所以{log2(an-1)}为等比数列