Combinational meaning of $\sum\limits_{k=r}^{n} {k \choose r }={{n+1} \choose r+1}$
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
115236
Calculate the sum of inverse values of ${n\choose 0}, {n\choose 1}, ... {n\choose n}$
68124
why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$
17375
When is the limit of a sum equal to the sum of limits?
72551
Proof that $\rho = \pm1$ implies linear combination
139842
Seeking a combinatorial proof $\sum\limits _{k=0}^n (n-2k)^2\binom{n}{k}=n\times 2^n$
30472
Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.
147887
When do we have $ \lim_{n\to\infty}\sum_{k=1}^{n^2}\frac{n^{r-1}}{n^r+k^r}0$?
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
140877
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
86426
calculate $\sum_{1\le i\le r}\frac{i+1} { r+1}{2r-i\choose r-i}{s+i-2\choose i}+\frac{1}{r+1}{2r\choose r}$?