For given $k,N\in\mathbb{N}$, how to compute $\sum_{i=0}^Ni^k$?
117837
Formula for the general Cavalieri Sum: $S_n(p)=\sum\limits_{k=1}^{n} k^p\,\,\,n, p\in\mathbb N$
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
345
Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
21000
Calculating $\sum_{k=1}^nk(k!)$ combinatorially
133955
Compute: $\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2n+2nk+n^2k}$
562
Formula for calculating $\sum_{n=0}^{m}nr^n$
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
140172
How to compute the Riemann sum of $x^n$ for any positive integer $n$?
108401
Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
88973
How do you calculate this sum $\sum_{n=1}^\infty nx^n$?
61850
Compute $\sum_{k=0}^{\infty}\frac{1}{2^{k!}}$
114575
If $\sum_{i=1}^k \dim F_i > n(k-1)$ then $\cap_{i=1}^k F_i \neq \{0\}$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$