Is $\sum_{k=0}^n \left(k+1\right)\left(C^n_k\right)^2 = \frac{n+2}{2} C^{2n}_n$ for any positive integer $n$?
140632
A problem on Binomial Theorem
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
30672
Show that $\sum\limits_{k=0}^n\binom{2n}{2k}^{\!2}-\sum\limits_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$
30338
How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$
5272
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
143365
Is $\sum_{i=1}^{n-1}i=\binom{n}{2}$?
104753
$\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?
84557
Using right-hand Riemann sum to evaluate the limit of $ \frac{n}{n^2+1}+ \cdots+\frac{n}{n^2+n^2}$
37007
Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$
42736
Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$?
77564
How to prove for each positive integer $n$, the sum of the first $n$ odd positive integers is $n^2$?
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
126105
Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $
57549
Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
118571
Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even?