query: Summation Problem involving Reciprocal Binomial coefficients. Find $\sum_{r=0}^n \frac{(-1)^r}{^nC_r}$
positive_passages.docid: 69498
positive_passages.text: What is $\sum_{r=0}^n \frac{(-1)^r}{\binom{n}{r}}$?
negative_passages.docid: 36361
negative_passages.text: How to calculate the summation $(\sum_{p = k}^{n} \binom{n}{p}) / 2^n$ quickly?
negative_passages.docid: 48446
negative_passages.text: Summation involving a factorial: $1 + \sum_{j=1}^{n} j!j$
negative_passages.docid: 150355
negative_passages.text: Finding sum of binomial series
negative_passages.docid: 19581
negative_passages.text: $\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$
negative_passages.docid: 91239
negative_passages.text: Sum of binomial coefficients involving $n,p,q,r$
negative_passages.docid: 79124
negative_passages.text: Proving $\binom {n-1}{r-1}=\sum_{k=0}^r(-1)^k\binom r k \binom{n+r-k-1}{r-k-1}$
negative_passages.docid: 57549
negative_passages.text: Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
negative_passages.docid: 46840
negative_passages.text: How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$
negative_passages.docid: 94784
negative_passages.text: $\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument
negative_passages.docid: 19914
negative_passages.text: Closed form for $\sum_{n=0}^{\infty} \binom{n+k}{k} x^n$ (Negative Binomial Theorem)
negative_passages.docid: 94060
negative_passages.text: Sum of square binomial coefficients
negative_passages.docid: 562
negative_passages.text: Formula for calculating $\sum_{n=0}^{m}nr^n$
negative_passages.docid: 76319
negative_passages.text: How to prove $\sum\limits_{r=0}^n \frac{(-1)^r}{r+1}\binom{n}{r} = \frac1{n+1}$?
negative_passages.docid: 14399
negative_passages.text: Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$
negative_passages.docid: 143047
negative_passages.text: find $\sum_{k=0}^{t}(-1)^k\binom{t}{k}^2$ for odd t then for even t
negative_passages.docid: 49936
negative_passages.text: Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$