请高手回答:数列极限的运算
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请高手回答:数列极限的运算
![请高手回答:数列极限的运算](/uploads/image/z/5025288-48-8.jpg?t=%E8%AF%B7%E9%AB%98%E6%89%8B%E5%9B%9E%E7%AD%94%EF%BC%9A%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90%E7%9A%84%E8%BF%90%E7%AE%97)
1)
lim [a1+n^2an]
=lim [1/2 + n^2/[n(n+1)]
=1/2+1
=3/2
2)
lim an
=lim [sn-s(n-1)]
=lim [n^2/(n+1) - (n-1)^2/n]
=lim [n^3- (n+1)(n-1)^2]/n(n+1)
=lim [n^2+n-1]/n(n+1)
=1
lim [a1+n^2an]
=lim [1/2 + n^2/[n(n+1)]
=1/2+1
=3/2
2)
lim an
=lim [sn-s(n-1)]
=lim [n^2/(n+1) - (n-1)^2/n]
=lim [n^3- (n+1)(n-1)^2]/n(n+1)
=lim [n^2+n-1]/n(n+1)
=1