$\sum_{i=0}^n {2n \choose 2i} = 2^{2n-1}$
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
59253
Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k} $
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
7083
Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
30472
Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
3341
Find $\sum_{r=1}^{3n-1}{ (-1)^{r-1}r\over{3n \choose r}}$, if $n$ is even
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
26446
Find the sum : $\displaystyle\sum_{i=0}^n \frac{2^i}{1+x^{2^{i}}}$
101017
What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
1125
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
91784
Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$