Sum of all products of $k$ members of the set $\{1, 2, 3, \cdots, n\}$
98941
Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?
132249
Sum of every $k$th binomial coefficient.
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
25338
Sum of $n$ integers from set of size $2n-1$ divides $n$
117862
Number of partitions of an $n$-element set into $k$ classes
7302
$\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
84010
Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
119107
Is it true that $\sum_{k=3}^{n}\binom{n}{k}\binom{k}{3} = \binom{n}{3}\binom{n-3}{k-3}$?
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
85222
Direct sum of finitely-many non-abelian groups
108807
Subset of a cartesian product
31766
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
11817
Proving that every set $A \subset \Bbb N$ of size $n$ contains a subset $B \subset A$ with $n | \sum_{b \in B} b$