已知数列an满足a1=3an+1=an^2+2an其中n=1,2,3……设bn=log2(an+1),求证数列是等比数列
问题描述:
已知数列an满足a1=3an+1=an^2+2an其中n=1,2,3……设bn=log2(an+1),求证数列是等比数列
答
证:b1=log2(a1+1)=log2(3+1)=log2(4)=2a(n+1)=an²+2ana(n+1)+1=an²+2an+1=(an+1)²b(n+1)=log2[a(n+1)+1]=log2[(an+1)²]=2log2(an+1)=2bnb(n+1)/bn=2,为定值.数列{bn}是以2为首项,2为公比的等比...