How to calculate the sum of sequence $$\frac{1}{\binom{n}{1}}+\frac{1}{\binom{n}{2}}+\frac{1}{\binom{n}{3}}+\cdots+\frac{1}{\binom{n}{n}}=?$$ How about its limit?
Calculate sums of inverses of binomial coefficients
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sequences-and-series
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2Is $C^{i}_j$ meant to be the binomial coefficient $i$ choose $j$, $\binom{i}{j}$, or a constant $C_n$ raised to different powers? – 2012-05-30
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2@Arturo: My guess is that $C_n^k$ is meant to be $\binom{n}k$, with the subscript and superscript interchanged for some reason. I’ve seen that reversal here at least once before. – 2012-05-30
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1Modified the title (note that there is no *infinite* series in this problem). – 2012-05-30
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1see [A003149](http://oeis.org/A003149) – 2012-05-30
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1See also http://www.fq.math.ca/Scanned/19-5/rockett.pdf (Theorem 1) and https://cs.uwaterloo.ca/journals/JIS/VOL7/Sury/sury99.pdf . – 2016-07-25