已知数列an的前n项的和为sn,且对任意n∈N有an+sn=n,设bn=an-1,求证数列bn是等比数列

Question

已知数列an的前n项的和为sn,且对任意n∈N有an+sn=n,设bn=an-1,求证数列bn是等比数列

Answer 1

an+sn=n a(n+1)+s(n+1)=n+1 a(n+1)-an+a(n+1)=1 a(n+1)-1=0.5(an-1)
即{an-1}是以a1-1=-0.5为首项 0.5为公比的等比数列