Let $k,l,n\in\mathbb{N}$ with $k+1\leq n$. Find a general formula for $\displaystyle\sum_{i=0}^l \dfrac{l\choose i}{n\choose {k+i}}$
67844
Prove equation with binomial coefficient
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
13098
Find a formula for $\sum\limits_{k=1}^n \lfloor \sqrt{k} \rfloor$
3341
Find $\sum_{r=1}^{3n-1}{ (-1)^{r-1}r\over{3n \choose r}}$, if $n$ is even
117837
Formula for the general Cavalieri Sum: $S_n(p)=\sum\limits_{k=1}^{n} k^p\,\,\,n, p\in\mathbb N$
107976
Find a closed formula for $\sum_{n=1}^\infty nx^{n-1}$
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
116722
Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
151757
Simplify $\sum_{i=0}^{N/2}{N-i\choose i}$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
86900
Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
86426
calculate $\sum_{1\le i\le r}\frac{i+1} { r+1}{2r-i\choose r-i}{s+i-2\choose i}+\frac{1}{r+1}{2r\choose r}$?