prove the equation by generating functions
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
65983
Combinatorial proof of binomial coefficient summation identity
12949
Inductive Proof of Euler's Formula $v-e+r=2$
115435
Induction: prove using congruences
90904
Combinatorial proof of an identity with squared binomial coefficients
27922
prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
27588
Generating functions and central binomial coefficient
121765
Semigroups and solutions of equation
58589
On the factorial equations $A! B! =C!$ and $A!B!C! = D!$
24785
How prove this equation $\alpha=\aleph_{0}\alpha$
55210
Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
100788
Proving Newton's identities
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
111779
Ordinary generating function for $\binom{3n}{n}$
14884
Compute a sum with partial fraction decomposition and generating functions
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
113068
Identity of moment-generating functions