Simplify the sum $\sum_{k=0}^{n} \binom{90}{n}p^n(1-p)^{90-n}$
93617
Sum of the product of two combinations
94784
$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument
98082
Another combinatorics problem: $\sum\limits_{k = 0}^n (-1)^k \binom{2n-k}k2^{2n-2k}=2n+1$
28027
Find $\sum_{k=0}^{n}4^k \binom{n}{k}$
99843
How to simplify $ \sum_{k=0}^{\infty} \binom{k + r - 1}{k} x^k$
19914
Closed form for $\sum_{n=0}^{\infty} \binom{n+k}{k} x^n$ (Negative Binomial Theorem)
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
37771
Sum of a power series $n x^n$
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
68848
How to simplify $\sum_{k=1}^nk\cdot k!$
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
140877
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
35381
Sum with binomial coefficients: $\sum_{k=1}^m  \frac{1}{k}{m \choose k} $
91239
Sum of binomial coefficients involving $n,p,q,r$
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
148949
Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
39909
Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$