How do you prove this very different method for evaluating $\sum_{k=1}^nk^p$
134721
A method for evaluating sums/discrete functions by assuming they can be made continuous and differentiable?
81729
Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion
121661
Evaluating the sum $\Sigma \, \frac{1}{k(k+p)}$
87320
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
158774
Series of binomial coefficients: $\sum\limits_{n=k}^{\infty}{\binom nk}x^n=\frac{x^k}{(1-x)^{k+1}}$
122534
Show that $\sum (-1)^{n+1}/n$ = $k$ can be expanded to a sum with $ 1 - 1/2 + 1/3 + 1/5 - 1/4 +1/7 + 1/9 - 1/6 + ....$ which is $3k/2$
158863
How to prove $\sum_p p^{-2} < \frac{1}{2}$?
345
Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
31766
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
19868
Evaluate: $ \sum _ {k=1}^{n}{\frac{k}{n}\binom{n}{k}t^k(1-t)^{n-k}}$
125712
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$