Exactly why coefficient of $x^ky^{n-k}$ is $C(k,n)$
52557
Derivation of binomial coefficient in binomial theorem.
42606
Orthogonality for Binomial Coefficients
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
104753
$\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?
55119
Proof that the coefficients of a polynomial are real
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
69943
why is ${n+1\choose k} = {n\choose k} + {n\choose k-1}$?
108401
Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
41354
Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
137983
Normalisation of $k[x,y]/(y^2-x^2(x-1))$
26233
$[K(\zeta_n):K]=\phi(n)$?
139074
Question about $a_n=\sum_{k=1}^n \frac{n}{n^2+k}\ $for $ n \in\mathbb{N}$
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction