Question

已知数列{an}满足a0=1,an=a0+a1+...+a(n-1), (n≥1),则当n≥1时，an=_

A.2^n B.n(n+1)/2 c.2^(n-1) D.2^n-1

Answer 1

a1=a0=1
a2=a1+a0=2 a2=2a1
a3=a2+a1+a0=2a2
a4=2a3
...............
an=2a(n-1)=2^2a(n-2)=2^(n-1)a1=2^(n-1)