{an}的前n项和Sn=(3n²+5n)/(n²+3n+2),求lim(n→+∞)[a(n+1)/an]的值等待妙招有刚看到题的不要管网友推荐,我会取消网友推荐的
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![{an}的前n项和Sn=(3n²+5n)/(n²+3n+2),求lim(n→+∞)[a(n+1)/an]的值等待妙招有刚看到题的不要管网友推荐,我会取消网友推荐的](/uploads/image/z/7126511-23-1.jpg?t=%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%3D%283n%26%23178%3B%2B5n%29%2F%28n%26%23178%3B%2B3n%2B2%29%2C%E6%B1%82lim%28n%E2%86%92%2B%E2%88%9E%29%5Ba%28n%2B1%29%2Fan%5D%E7%9A%84%E5%80%BC%E7%AD%89%E5%BE%85%E5%A6%99%E6%8B%9B%E6%9C%89%E5%88%9A%E7%9C%8B%E5%88%B0%E9%A2%98%E7%9A%84%E4%B8%8D%E8%A6%81%E7%AE%A1%E7%BD%91%E5%8F%8B%E6%8E%A8%E8%8D%90%2C%E6%88%91%E4%BC%9A%E5%8F%96%E6%B6%88%E7%BD%91%E5%8F%8B%E6%8E%A8%E8%8D%90%E7%9A%84)
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{an}的前n项和Sn=(3n²+5n)/(n²+3n+2),求lim(n→+∞)[a(n+1)/an]的值等待妙招有刚看到题的不要管网友推荐,我会取消网友推荐的
{an}的前n项和Sn=(3n²+5n)/(n²+3n+2),求lim(n→+∞)[a(n+1)/an]的值
等待妙招
有刚看到题的不要管网友推荐,我会取消网友推荐的
{an}的前n项和Sn=(3n²+5n)/(n²+3n+2),求lim(n→+∞)[a(n+1)/an]的值等待妙招有刚看到题的不要管网友推荐,我会取消网友推荐的
Sn=(3n^2+9n+6-4n-6)/(n^2+3n+2)=3-2(2n+3)/(n+1)(n+2)
=3-2(1/(n+1)+1/(n+2)) 关键点
S(n-1)=3-2(1/n+1/(n+1))
an=Sn-S(n-1)=2(1/n-1/(n+2))
a(n+1)=2(1/(n+1)-1/(n+3))
a(n+1)/an=(1/(n+1)-1/(n+3))/(1/n-1/(n+2))
=n(n+2)/((n+1)(n+3))=(n^2+2n)/(n^2+4n+3)
=(1+2/n)/(1+4/n+3/n^2)
lima(n+1)/an=1