List questions from binomial-theorem | MathQa

Show that the interest rate sequence is Cauchy

Published on 12 Jan 2025 - 22:33

Binomial theorem to find coeff of $x^n$

Published on 12 Jan 2025 - 22:30

How to prove that $\sum_{i=0}^n\frac{(a;q)_i}{(q;q)_i}\frac{(b;q)_{n-i}}{(q;q)_{n-i}}a^{n-i}=\frac{(ab;q)_n}{(q;q)_n}$?

Published on 12 Jan 2025 - 22:53

Is a binomial expansion of the denominator valid here?

Published on 30 Dec 2024 - 7:51

approximate $\sum_{k=0}^n {n \choose k} k! n^{-k} \sim {\sqrt{\pi n}\over \sqrt{2}}$

Published on 12 Jan 2025 - 22:45

On the binomial series $(1+\frac{1}{8n})^{1/2}$, where $n$ is an even perfect number

Published on 02 Jan 2025 - 11:50

Prove that sum $(\sqrt2+1)^n+(\sqrt2-1)^n$ is rational for even numbers

Published on 12 Jan 2025 - 22:47

Prove: ${n\choose 1}-3{n\choose 3}+9{n\choose 5}-...=\frac{-1}{\sqrt{3}}(-2)^n\sin\frac{2n\pi}{3}$

Published on 12 Jan 2025 - 22:51

Proving a binomial identity

Published on 12 Jan 2025 - 18:05

Binomial theorem and it's geometric interpretation with functions

Published on 12 Jan 2025 - 22:45