Proof of $\sum_{0 \le k \le a} {a \choose k} {b \choose k} = {a+b \choose a}$
42763
How to prove Vandermonde's Identity: $\sum_{k=0}^{n}\binom{R}{k}\binom{M}{n-k}=\binom{R+M}{n}$?
13026
Prove that if AB=I_m, then rk(A)=rk(B).
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
44621
Simple binomial theorem proof: $\sum_{j=0}^{k} \binom{a+j}j = \binom{a+k+1}k$
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
142534
Proof of $k {n\choose k} = n {n-1 \choose k-1}$ using direct proof
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
49066
Give the combinatorial proof of the identity $\sum\limits_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k}$
89576
Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
74887
Combinatorial proof of the identity ${n+1\choose k+1}={k\choose k}+{k+1\choose k}+...+{n-1\choose k}+{n\choose k}$