How to use the generalized binomial theorem to produce the power series of $(1-x)^{1/2}$
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
151384
Summation of series involving binomial coefficients and polynomial of degree at most n-1
36799
Maclaurin series for $\frac{x}{e^x-1}$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
143927
Binomial coefficients that are powers of 2
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
64328
How to prove that the Binet formula gives the terms of the Fibonacci Sequence?
130548
What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?
122024
Asymptotic of a sum involving binomial coefficients
133420
Computing the binomial series: $\binom{n}{2}\cdot2^2+\binom{n}{4}\cdot2^4+\binom{n}{6}\cdot2^6+\cdots+ \binom{n}{n}\cdot2^n$
4931
variation of the binomial theorem
140632
A problem on Binomial Theorem
63829
Use Cauchy product to find a power series represenitation of $1 \over {(1-x)^3}$
19868
Evaluate: $ \sum _ {k=1}^{n}{\frac{k}{n}\binom{n}{k}t^k(1-t)^{n-k}}$
74664
A question regarding power series expansion of an entire function
158774
Series of binomial coefficients: $\sum\limits_{n=k}^{\infty}{\binom nk}x^n=\frac{x^k}{(1-x)^{k+1}}$
155769
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$