已知数列{an}满足a0=1,an=a0+a1+…+an-1n≥1、,则当n≥1时,an=(  ) A.2n B.n(n+1)2 C.2n-1 D.2n-1

问题描述:

已知数列{an}满足a0=1,an=a0+a1+…+an-1n≥1、,则当n≥1时,an=(  )
A. 2n
B.

n(n+1)
2

C. 2n-1
D. 2n-1

∵数列{an}满足a0=1,an=a0+a1+…+an-1(n≥1),
则a1=a0=1=20
a2=a0+a1=2=21
a3=a0+a1+a2=4=22

由此猜想当n≥1时,an=2n-1
故答案应选:C