问题
选择题
已知数列{log2(an-1)}(n∈N*)为等差数列,且a1=3,a2=5,则
|
答案
数列{log2(an-1)}(n∈N*)为等差数列,
设其公差为d,则log2(an-1)-log2(an-1-1)=d,
即
=2d,又由a1=3,a2=5,an-1 an-1-1
则d=1,即
=2,an-1 an-1-1
{an-1}是以a1-1=2为首项,公比为2的等比数列,
进而可得,an-1=2n,则an=2n+1,
故an-an-1=2n-2n-1=2n-1,
则
(lim n→∞
+1 a2-a1
+…+1 a3-a2
)=1 an+1-an
(lim n→∞
+1 2
+…+1 4
)=1,1 2n-1
故选C.