How to evaluate the sum $\sum_{k = 0}^{n}2^k {{n}\choose {k}}$
5801
Combinatorial proof help
102942
Compute the sum $\sum_{k=1}^{\infty}k^mz^k$ where $|z|<1$
5054
Calculate $\sum\limits_{k=0}^{\infty}\frac{1}{{2k \choose k}}$
913
Evaluating $\sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}$
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
26446
Find the sum : $\displaystyle\sum_{i=0}^n \frac{2^i}{1+x^{2^{i}}}$
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
94143
Evaluate:: $ 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right) $
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
117200
Evaluation of $ \sum_{k=0}^n \cos k\theta $
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
148949
Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$