各项均为正数且公差为1的等差数列an,前n项和为Sn,求limSn/an×an+1
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![各项均为正数且公差为1的等差数列an,前n项和为Sn,求limSn/an×an+1](/uploads/image/z/5496360-24-0.jpg?t=%E5%90%84%E9%A1%B9%E5%9D%87%E4%B8%BA%E6%AD%A3%E6%95%B0%E4%B8%94%E5%85%AC%E5%B7%AE%E4%B8%BA1%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97an%2C%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E6%B1%82limSn%2Fan%C3%97an%2B1)
各项均为正数且公差为1的等差数列an,前n项和为Sn,求limSn/an×an+1
各项均为正数且公差为1的等差数列an,前n项和为Sn,求limSn/an×an+1
各项均为正数且公差为1的等差数列an,前n项和为Sn,求limSn/an×an+1
设首项为a1,d=1
前n项和为Sn=na1+n(n-1)d/2=na1+n(n-1)/2
an=a1+(n-1)d=a1+n-1
limSn/an×an+1=lim[na1+n(n-1)/2]/(a1+n-1)(a1+n-1)+1
=lim[a1/n+1/2-1/(2n)]/[(a1/n+1-1/n)^2+1/(n^2)]
=1/2
答案为1/2
1/2