Question

已知数列,a1=1,ana(n+1)=2^n,求an

Answer 1

a1=1,ana(n+1)=2^n

a1a2=2^1 a2=2

a2a3=2^2 a3=2

a3a4=2^3 a4=2^2

a4a5=2^4 a5=2^2

a5a6=2^5 a6=2^3

a6a7=2^6 a7=2^3

.

n为奇数时 an=2^((n-1)/2) an+1=2^((n-1)/2+1)=2^((n+1)/2)

n为偶数时 an=2^(n/2) an+1=2^(n/2)