Evaluate $\sum^{n-1}_{k=1} {n\choose k}\frac{kn^{n-k}}{k+1}$
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
13236
Proving equality - a sum including binomial coefficient $\sum_{k=1}^{n}k{n \choose k}2^{n-k}=n3^{n-1}$
129801
Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
137249
find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$
91933
Evaluate $\sum_{k=1}^nk\cdot k!$
43509
Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$
17872
Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
76828
Evaluating $\sum_{i = 0}^{\lfloor n/2 \rfloor} {n \choose 2i}p^{2i}(1 - p)^{n - 2i}$
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
121661
Evaluating the sum $\Sigma \, \frac{1}{k(k+p)}$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
134610
Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
81654
Evaluate $\lim_{n\to\infty} [{1\over kn}+{1\over k(n+1)}+{1\over k(n+2)}+\cdots+{1\over k(n+p-k)}]$ where $k<p$
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$