What is $\sum_{k=1}^n{{n}\choose{k}}k^{3}$ equal to?
115433
Find the summation of given expression: $\sum_{k=1}^n k^3\binom nk$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
92704
Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
5272
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
112005
Showing that if $p_1 + \cdots p_n = 1$ then $\displaystyle \sum_{k=1}^n \left(p_k + \dfrac {1}{p_k} \right)^2 \ge n^3+2n+\dfrac 1n$?
143365
Is $\sum_{i=1}^{n-1}i=\binom{n}{2}$?
151757
Simplify $\sum_{i=0}^{N/2}{N-i\choose i}$
87320
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
7302
$\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?
153231
Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$?
142666
Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
96700
How is $\dfrac1{(1-x)^5}=\sum_{n\geq0}{n+4\choose4}x^n$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
104753
$\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?