已知数列{log2(an-1)}(n∈N*)为等差数列,且a1=3,a3=9.
(1)求数列{an}的通项公式;
(2)证明:
+…+
<1.
已知数列{log2(an-1)}(n∈N*)为等差数列,且a1=3,a3=9.
(1)求数列{an}的通项公式;
(2)证明:+…+<1.
(1)解设等差数列{log2(an-1)}的公差为d.由a1=3,a3=9,得log22+2d=log28,即d=1.
∴log2(an-1)=1+(n-1)×1=n,即an=2n+1.
(2)证明
,
+…+
=
+…+
=
=1-<1.