How can we prove this? Any help would be appreciated.
real-analysisinequalitylimsup-and-liminf
asked 2011-10-02
user id:17043
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$ h \in $ what? – 2011-10-03
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Thomas, it is very rare for a thread on math.stackexchange to have no activity for 2 hours, plenty of us are willing to help you as long as you show us some effort and work you have done! – 2011-10-03
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To expand on Mark's comment: What is $h$ in your formula? Is this a sequence, so that $h=1,2,3,\ldots$? – 2011-10-03
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In general, to prove that lim sup (whatever) is less than or equal to (something), it suffices to prove that for every $\epsilon > 0$, eventually (whatever) is less than (something + $\epsilon$). Here "eventually" means when $h$ is sufficiently large, if you want $h\to\infty$, or else $|h-a|$ is sufficiently small, if you want $h\to a$. – 2011-10-03
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