What is the finite sum of an alternating odd sequence with binomial coefficients: $ \ \sum_{k=0}^{j} \binom{j}{k} \ \frac{(-1)^k}{2k+1}$?
64378
Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
17551
Truncated alternating binomial sum
113770
Sum of alternating series $\sum_{i=1}^n \frac{(-1)^{i-1}}{2i-1}$ with accuracy of $\pm .05$.
32791
Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$
125712
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
57549
Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
31970
Alternating sum of squares of binomial coefficients
142303
Alternating sum of binomial coefficients multiplied by (1/k+1)
83400
Sum of products of binomial coefficients: $ \sum_{l=0}^{n-j} \binom{M-1+l}{l} \binom{n-M-l}{n-j-l} = \binom{n}{j} $
439
Alternating binomial sum with intervals of two
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
6436
Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
19914
Closed form for $\sum_{n=0}^{\infty} \binom{n+k}{k} x^n$ (Negative Binomial Theorem)
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
2584
Convergence of an alternating series : $ \sum_{n\geq 1} \frac{(-1)^n|\sin n|}{n}$