已知数列{an},an∈N*,前n项和Sn=1/8(an+2)2. (1)求证:{an}是等差数列; (2)若bn=1/2an-30,求数列{bn}的前n项和的最小值.

问题描述:

已知数列{an},an∈N*,前n项和Sn=

1
8
(an+2)2
(1)求证:{an}是等差数列;
(2)若bn=
1
2
an-30,求数列{bn}的前n项和的最小值.

(1)证明:∵an+1=Sn+1-Sn=18(an+1+2)2-18(an+2)2,∴8an+1=(an+1+2)2-(an+2)2,∴(an+1-2)2-(an+2)2=0,(an+1+an)(an+1-an-4)=0.∵an∈N*,∴an+1+an≠0,∴an+1-an-4=0.即an+1-an=4,∴数列{an...