设无穷等差数列{an}的前n项和为Sn,若不等式 对任意正整数n都成立,则实数λ的最大值是( )
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设无穷等差数列{an}的前n项和为Sn,若不等式 对任意正整数n都成立,则实数λ的最大值是( )
A.1 B.2 C.3 D.5
![](http://img.wesiedu.com/upload/1/ec/1ecddf56b1629b7bfe1f3a5342076b22.jpg)
A.1 B.2 C.3 D.5
![](http://img.wesiedu.com/upload/1/ec/1ecddf56b1629b7bfe1f3a5342076b22.jpg)
![设无穷等差数列{an}的前n项和为Sn,若不等式 对任意正整数n都成立,则实数λ的最大值是( )](/uploads/image/z/4792944-48-4.jpg?t=%E8%AE%BE%E6%97%A0%E7%A9%B7%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E8%8B%A5%E4%B8%8D%E7%AD%89%E5%BC%8F+%E5%AF%B9%E4%BB%BB%E6%84%8F%E6%AD%A3%E6%95%B4%E6%95%B0n%E9%83%BD%E6%88%90%E7%AB%8B%2C%E5%88%99%E5%AE%9E%E6%95%B0%CE%BB%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF%EF%BC%88+%EF%BC%89)
A:1
Sn=n(a1+an)/2,
an^2+Sn^2/n^2=an^2+[(a1+an)/2]^2=[5an^2+2a1*an+a1^2]/4
=(5/4)[an^2+(2/5)a1*an+a1^2/25]+a1^2/5
=(5/4)[an+a1/5]^2+a1^2/5
故应有(5/4)[an+a1/5]^2+a1^2/5>=λa1^2/5
由an的任意性知,λ=1
再问: = =.你怎么跟我选的一样,答案选A,1
Sn=n(a1+an)/2,
an^2+Sn^2/n^2=an^2+[(a1+an)/2]^2=[5an^2+2a1*an+a1^2]/4
=(5/4)[an^2+(2/5)a1*an+a1^2/25]+a1^2/5
=(5/4)[an+a1/5]^2+a1^2/5
故应有(5/4)[an+a1/5]^2+a1^2/5>=λa1^2/5
由an的任意性知,λ=1
再问: = =.你怎么跟我选的一样,答案选A,1
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