The following problem appeared in Volume 96, Issue 3 (2023) of Mathematics Magazine. Let $latex A_1, \dots, A_n$ be arbitrary events in a probability field. Denote by $latex B_k$ the event that at least $latex k$ of $latex A_1, \dots A_n$ occur. Prove that $latex \displaystyle \sum_{k=1}^n P(B_k) = \sum_{k=1}^n P(A_k)$. I'll admit when I…

Mean Green Math

17.01.2025

Solving Problems Submitted to MAA Journals (Part 5a) – Mean Green Math

The following problem appeared in Volume 96, Issue 3 (2023) of Mathematics Magazine. Evaluate the following sums in closed form: $latex \displaystyle \sum_{n=0}^\infty \left( \cos x - 1 + \frac{x^2}{2!} - \frac{x^4}{4!} \dots + (-1)^{n-1} \frac{x^{2n}}{(2n)!} \right)$ and $latex \displaystyle \sum_{n=0}^\infty \left( \sin x - x + \frac{x^3}{3!} - \frac{x^5}{5!} \dots + (-1)^{n-1} \frac{x^{2n+1}}{(2n+1)!} \right)$.…

Mean Green Math

24.01.2025

Solving Problems Submitted to MAA Journals (Part 5b) – Mean Green Math

The following problem appeared in Volume 96, Issue 3 (2023) of Mathematics Magazine. Evaluate the following sums in closed form: $latex f(x) = \displaystyle \sum_{n=0}^\infty \left( \cos x - 1 + \frac{x^2}{2!} - \frac{x^4}{4!} \dots + (-1)^{n-1} \frac{x^{2n}}{(2n)!} \right)$ and $latex g(x) = \displaystyle \sum_{n=0}^\infty \left( \sin x - x + \frac{x^3}{3!} - \frac{x^5}{5!} \dots…

Mean Green Math

31.01.2025

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Solving Problems Submitted to MAA Journals (Part 4) – Mean Green Math

Solving Problems Submitted to MAA Journals (Part 5a) – Mean Green Math

Solving Problems Submitted to MAA Journals (Part 5b) – Mean Green Math

Solving Problems Submitted to MAA Journals (Part 5c) – Mean Green Math

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Mean Green Math