Compute $\sum_{k=0}^{n}\frac{1}{\binom{n}{k}}$
115236
Calculate the sum of inverse values of ${n\choose 0}, {n\choose 1}, ... {n\choose n}$
30672
Show that $\sum\limits_{k=0}^n\binom{2n}{2k}^{\!2}-\sum\limits_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
142303
Alternating sum of binomial coefficients multiplied by (1/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}$
104704
Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
116491
Closed form for $\sum_{k=0}^{m} {\binom {m}{k}} a^{k} (b+ck)^N$
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
57549
Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
131326
How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
79814
Calculate sums of inverses of binomial coefficients
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?