用N-ε語(yǔ)言
對(duì)于任意ε>0
存在N=max(1,5/2ε)
當(dāng)n>N時(shí)
|(3n^2+n)/(2n^2-1)-3/2|
=|(6n^2+2n-6n^2+3)/[2(2n^2-1)]|
=(2n+3)/[2(2n^2-1)]
因?yàn)閚>N>=1,所以2n+3<2n+3n=5n
2n^2-1>2n^2-n^2=n^2
(分子更大,分母更小的數(shù)更大)
<5n/[2(n^2)]
=5/2n
<5/2(5/2ε)
=ε
由極限定義
lim n->∞ (3n^2+n)/(2n^2-1)=3/2