Summation of Combinations leads to $2^n$
23557
Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
73258
Power series summation
33104
Combinatorial Proof with Summation Identity
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
109599
A finite sum involving the binomial coefficients and the harmonic numbers
146200
proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
57986
Sum of products of combinatorials
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
143501
Find all $n\in\mathbb N^+$ such that the sum of the digits of $5^n$ is equal to $2^n$.
138456
How to fit $\sum{n^{2}x^{n}}$ into a generating function?
65843
Number of possible combinations of x numbers that sum to y
72402
Summation of natural number set with power of $m$
142132
How do you prove $\sum \frac {n}{2^n} = 2$?
37771
Sum of a power series $n x^n$
21000
Calculating $\sum_{k=1}^nk(k!)$ combinatorially