Prove that $^nC_r = {^{n - 1}C_r} + {^{n - 1}C_{r - 1}}$
91648
Binomial coefficient proof
146533
Having problems proving $ \sum_{r=0}^{n}(r+1) \binom{n}{r} = (n+2)2^{n-1} $
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
94383
Prove that $A^TD-C^TB=I$
25967
Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$
141909
Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
14986
Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$
62254
Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
142347
What is the highest power of $n$ in $(n^r-1)!$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
53866
Prove $ x^n-1=(x-1)(x^{n-1}+x^{n-2}+...+x+1)$
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
153506
Proving the inverse of a matrix equals $I_n-\frac{1}{n-1}A$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$