Sum of binomial coefficients $\binom{n-k}{k}$ and Fibonacci numbers
131400
Solution check: Let $f_n$ be fibonacci numbers. Prove: $\sum_{k=0}^{n-1} \binom{n+k}{2k+1} = f_{2n-1}$ and $\sum_{k=0}^n \binom{n+k}{2k} = f_{2n}$
133420
Computing the binomial series: $\binom{n}{2}\cdot2^2+\binom{n}{4}\cdot2^4+\binom{n}{6}\cdot2^6+\cdots+ \binom{n}{n}\cdot2^n$
57549
Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
64378
Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
59638
How to prove this result on binomial coefficients?
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
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} $
150355
Finding sum of binomial series
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
142994
How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?
134361
Calculating the sum of a binomial coefficient series
137215
Cesaro identity for Fibonacci numbers: $ F_{2n} = \sum_{k=1}^n \binom{n}{k} F_k$
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
79814
Calculate sums of inverses of binomial coefficients
70248
Closed-form expression for $\sum_{k=0}^n\binom{n}kk^p$ for integers $n,\,p$
116491
Closed form for $\sum_{k=0}^{m} {\binom {m}{k}} a^{k} (b+ck)^N$