The sum $\sum_{k=0}^{n} (-1)^k \frac{{n \choose k}}{{n+k \choose k}}=\frac{1}{2}$
93813
How to show that $\sum\limits_{k=0}^n (-1)^k\tfrac{{ {n}\choose{k}}}{{ {x+k}\choose{k}}} = \frac{x}{x+n}$
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
32791
Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
30472
Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
19868
Evaluate: $ \sum _ {k=1}^{n}{\frac{k}{n}\binom{n}{k}t^k(1-t)^{n-k}}$
138542
Evaluating sums question $\sum_{k=2}^n \frac{1}{k^2-1}$
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
72639
Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
142985
Finding sum of series $\sum^{\infty}_{k=0}\frac{(k+1)(k+2)}{2^k}$
140877
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
134610
Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
29524
Formula for the sum $\sum_{i=2}^{n} \frac1{i^2-1}$
143047
find $\sum_{k=0}^{t}(-1)^k\binom{t}{k}^2$ for odd t then for even t