List questions from binomial-theorem | MathQA

Sum with binomial coefficient using identity

Published on 11 Jan 2023 - 18:14

I would like to prove that $e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = \sum_{k=0}^{+\infty}\frac{1}{k!}.$

Published on 11 Jan 2023 - 19:34

Find all rational terms of $(\sqrt{2}+\sqrt[3]{3})^{100}$

Published on 18 Jan 2023 - 16:03

How to show that $12^{12} + 9^{9}$ can be divided by $15$ using Binomial Theorem?

Published on 24 Jan 2023 - 1:44

On the sum: $\sum_{i = 0}^n i {n \choose i} = n 2^{n-1}$

Published on 27 Jan 2023 - 10:44