已知正数列{an}和{bn}满足:对任意n(n属于N*),an,bn,an+1成等差数列且an+1=根号下b
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已知正数列{an}和{bn}满足:对任意n(n属于N*),an,bn,an+1成等差数列且an+1=根号下b
已知正数列{an}和{bn}满足:对任意n(n属于N*),an,bn,a(n+1)成等差数列且a(n+1)=根号下bn x b(n+1)
判断数列根号下bn为等差数列
已知正数列{an}和{bn}满足:对任意n(n属于N*),an,bn,a(n+1)成等差数列且a(n+1)=根号下bn x b(n+1)
判断数列根号下bn为等差数列
an,bn,an+1成等差数列,则有:2bn=an+a(n+1)
由题意:
a(n+1)=根号bn x b(n+1)
a(n)=根号b(n-1) x b(n)
将上两式代入:2bn=an+a(n+1) ,有
2bn=根号bn x b(n+1)+根号b(n-1) x b(n)
因为根号bn为正数,上式两端同除以根号bn,得:
2倍的根号bn=根号 b(n+1)+根号b(n-1)
由此,上式足以说明根号下bn为等差数列!
由题意:
a(n+1)=根号bn x b(n+1)
a(n)=根号b(n-1) x b(n)
将上两式代入:2bn=an+a(n+1) ,有
2bn=根号bn x b(n+1)+根号b(n-1) x b(n)
因为根号bn为正数,上式两端同除以根号bn,得:
2倍的根号bn=根号 b(n+1)+根号b(n-1)
由此,上式足以说明根号下bn为等差数列!
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