Simplifying Expression $\sum\limits_{x=1}^{k} {N - x \choose k - x} x^2$
57549
Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
139842
Seeking a combinatorial proof $\sum\limits _{k=0}^n (n-2k)^2\binom{n}{k}=n\times 2^n$
84595
How to evaluate $\lim\limits_{n\to+\infty} \prod\limits_{k=1}^n (1+k/n^2)$?
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
115433
Find the summation of given expression: $\sum_{k=1}^n k^3\binom nk$
146651
Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$
143207
What is $\sum\limits_{i=1}^n \sqrt i\ $?
155382
Find $ \lim\limits_{{n \to \infty}} \frac1{2^n} \sum\limits_{k=1}^n \frac1{\sqrt{k}} \binom nk$
156814
Compute the limit of the sequence ${\textstyle\sum_{k=1}^n}\frac1{\sqrt{n^2+k}}$
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
153465
Is there a closed form expression for $1 + x + x^{4} + x^{9}+x^{16}+x^{25} +..+x^{k^2}$?
158774
Series of binomial coefficients: $\sum\limits_{n=k}^{\infty}{\binom nk}x^n=\frac{x^k}{(1-x)^{k+1}}$
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 $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
118024
Simplify the expression $\binom{n}{0}+\binom{n+1}{1}+\binom{n+2}{2}+\cdots +\binom{n+k}{k}$
118436
Identifying the series $\sum\limits_{k=-\infty}^{\infty} 2^k x^{2^k}$