Need help with the sum of the binomial coefficients: ${k+l \choose l}$
36786
Prove $\sum\limits_{i=0}^n\binom{i+k-1}{k-1}=\binom{n+k}{k}$ (a.k.a. Hockey-Stick Identity)
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
144571
A conjecture including binomial coefficients
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
94784
$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument
154703
Use combinatorics to prove $L\left(n,k\right)=\sum_{j=0}^{n}{ n\brack j}{j\brace k}$
115686
A finite summation of double binomial coefficients
155496
sum of combinations $\binom n{0} + \binom n{3} + \binom n{6} +... +\binom n{3k}$
115236
Calculate the sum of inverse values of ${n\choose 0}, {n\choose 1}, ... {n\choose n}$
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
57986
Sum of products of combinatorials
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
81729
Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion
116491
Closed form for $\sum_{k=0}^{m} {\binom {m}{k}} a^{k} (b+ck)^N$
56828
A combinatorial proof that the alternating sum of binomial coefficients is zero