设{an}是正数组成的数列,其前n项和为Sn,并且对于所有的n N+,都有

设{an}是正数组成的数列,其前n项和为Sn,并且对于所有的n N+,都有

(1)写出数列{an}的前3项;

(2)求数列{an}的通项公式(写出推证过程);

(3)设是数列{bn}的前n项和,求使得对所有n N+都成立的最小正整数的值。

答案

⑶m的最小值是10


解析:

(1)  n=1时      ∴

n=2时         ∴

n=3时     ∴    

(2)∵   ∴

两式相减得:   即

也即

    ∴  即是首项为2,公差为4的等差数列

 

(3)

     

对所有都成立   ∴  即

故m的最小值是10 。

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