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| (3n+1)/(2n+1) - 3/2 |<ε
| [2(3n+1)-3(2n+1) ]/[2(2n+1)] |<ε
| -1/[2(2n+1)] |<ε
1/[2(2n+1)]<ε
2n+1 > 1/(2ε)
n >1/(4ε)
选 N=[1/(4ε)] +1
∀ε>0, ∃N=[1/(4ε)] +1 , st
| (3n+1)/(2n+1) - 3/2 |<ε , ∀n>N
=>
lim(n->∞) (3n+1)/(2n+1) =3/2
| [2(3n+1)-3(2n+1) ]/[2(2n+1)] |<ε
| -1/[2(2n+1)] |<ε
1/[2(2n+1)]<ε
2n+1 > 1/(2ε)
n >1/(4ε)
选 N=[1/(4ε)] +1
∀ε>0, ∃N=[1/(4ε)] +1 , st
| (3n+1)/(2n+1) - 3/2 |<ε , ∀n>N
=>
lim(n->∞) (3n+1)/(2n+1) =3/2
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谢谢！
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