Question

已知数列an满足a1=a2=a3=2,an+1（n+1为角标）=a1a2a3……an-1,记b(n-2)=a^2+a2^

Answer 1

an+1=a1a2a3……an-1 an=a1a2a3……an-2 an+1/an=an-1/an-2

a2/a1=1 a3/a2=1 a4/a3=a3/a2=1 a5/a4=a4/a3=1 ……an/an-1=an-a/an-2=……=1

an=2

bn=a^2+a2^2+…+an^2-a1a2…an=n*2^2-2^n