$\sum_{x+y =c}{a\choose x}{b\choose y} = {a+b\choose c}$
42763
How to prove Vandermonde's Identity: $\sum_{k=0}^{n}\binom{R}{k}\binom{M}{n-k}=\binom{R+M}{n}$?
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
14410
If $(1+ \cos A) (1+ \cos B) (1+\cos C)= y = (1- \cos A) (1-\cos B) (1-\cos C)$ then $y = \pm \sin A \sin B \sin C$
133480
new addition and new multiplication x ⊕ y = x + y − 1, x ⊗ y = x + y − xy on set Z, prove the set Z equipped with these 2 new operation
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
52305
Is there a general relation between $a/b$ and $(a+c)/(b+c)$ where $a,b,c > 0 $?
23603
Joint distribution of $X+Y$ and $\frac{X}{X+Y}$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
49211
Solving $f(x+y) = f(x)f(y)f(xy)$
24856
Proving sup(A + B) = sup A + sup B
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
101394
Please explain the logic behind $d(xy) = y(dx) + x(dy)$
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
140877
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
77510
$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$