数列极限的证明如何证明lim((n+2)/(n^2-2))sin n=0
问题描述：
数列极限的证明
如何证明lim((n+2)/(n^2-2))sin n=0
答
|((n+2)/(n^2-2))sin n-0|
＜((n+2)/(n^2-4))sin n
=(sin n)/(n-2)
≤1/(n-2)
＜(1+2）/[(n-2)+2]
=3/n
答
lim(n+2)/(n^2-2)=lim(1/n+2/n^2)/(1-2/n^2)=0.
又|((n+2)/(n^2-2))sin n|