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This is from so called ratio test, which says

The series Ʃa(n) diverges if abs{a(n+1)/a(n)} ≥ 1 for n≥N where N is some fixed integer.

I was wondering if I could replace the condition with lim inf abs{a(n+1)/a(n)} ≥ 1.

So basically what I'm asking is whether these two below are equivalent or not.

1. abs{a(n+1)/a(n)} ≥ 1 for n≥N where N is some fixed integer

2. lim inf abs{a(n+1)/a(n)} ≥ 1

*a(n) means nth term in the sequence, and abs means absolute value.

Thank you in advance.

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# Could you check if these two are equivalent?

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