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lim inf (a _(n+1) / a_n) <= lim inf (a_n)^(1/n) <= lim sup (a_n)^(1/n)

<= lim sup(a_(n+1) / a_n).

Give examples where equality does not hold.

Is lim sup always >= lim inf? I am having trouble understanding these concept and proving things about them without specific numbers.