Question

已知an+1=2的n次方an,a1=2,求an通项

Answer 1

累乘即可

a(n+1)/an=2^n

则an=a1*(a2/a1)*(a3/a2)*……*(an/a(n-1)

=2*2*2^2*2^3*……*2^(n-1)

=2^(1+1+2+3+……+(n-1))

=2^(1+n(n-1)/2)

=2^((n^2-n+2)/2)