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
答
∵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