分类：教育/科学-理工学科-数学
问题：求数列极限见附件。我的想法是用夹逼准则，但是放缩不好。请各位大神 
见附件。我的想法是用夹逼准则，但是放缩不好。请各位指点。在线等。
回答：f(n)=√n[(n^2+1)^(1/4)-(n+1)^(1/2)]
=√n[(n^2+1)^(1/4)-(n^2+2n+1)^(1/4)]
=√n[(n^2+1)^(1/2)-(n^2+2n+1)^(1/2)]/[(n^2+1)^(1/4)+(n^2+2n+1)^(1/4)]
=√n[(n^2+1)-(n^2+2n+1)/[(n^2+1)^(1/4)+(n^2+2n+1)^(1/4)][(n^2+1)^(1/2)+(n^2+2n+1)^(1/2)]
=-2n^(3/2)/[(n^2+1)^(1/4)+(n^2+2n+1)^(1/4)][(n^2+1)^(1/2)+(n^2+2n+1)^(1/2)]
→-2/(1+1)(1+1)
=-1/2


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