已知{an}是正数组成的数列,a1=1,且点(,an+1)(n∈N*)在函数y=x2+1的图象上.(Ⅰ)求数列{an}的通项公式;(Ⅱ)若列数{bn}满足b1=1,bn+1=bn+2an,求证:bn ·bn+2<b2n+1.
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已知{an}是正数组成的数列,a1=1,且点(,an+1)(n∈N*)在函数y=x2+1的图象上.(Ⅰ)求数列{an}的通项公式;(Ⅱ)若列数{bn}满足b1=1,bn+1=bn+2an,求证:bn ·bn+2<b2n+1.