(Problem Solving) Proving $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\frac{1}{k+m+1}=\sum_{k=0}^{m}(-1)^k\binom{m}{k}\frac{1}{k+n+1}$
43066
Finding value of $S-T$ in $2$ binomial sum.
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
146533
Having problems proving $ \sum_{r=0}^{n}(r+1) \binom{n}{r} = (n+2)2^{n-1} $
94784
$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
48434
Prove that $\sum\limits_{k=0}^m\binom{m}k\binom{n}{r+k}=\binom{m+n}{m+r}$ using combinatoric arguments.
156566
Combinatorial proof of a binomial identity: $\sum_k \binom {2r} {2k-1}\binom{k-1}{s-1} = 2^{2r-2s+1}\binom{2r-s}{s-1}$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
107397
Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
106965
How to algebraically prove $\binom{n+m}{2} = nm + \binom{n}{2} + \binom{m}{2}$?
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
60860
Combinatorial proof of $\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$ and then use result to find a formula for $1^2 + 2^2 + \ldots + n^2$
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$