Is there a good lower bound for the tail of sums of binomial coefficients, so a lower bound for $\sum_{i=1}^k {n \choose 2i-1}$?
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1Wait, why are you only summing the $\binom{n}{j}$ with $j$ odd? – Sam Hopkins Oct 27 '20 at 18:41
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Summing over odd indices is equivalent to decreasing $n$ by 1, so this isn't any more complex than the basic tail-sum. – user44191 Oct 27 '20 at 23:51