Factorial Notation | 阶乘记法

📚 Factorial Notation | 阶乘记法

Factorial notation is a compact way of writing the product of consecutive positive integers. It appears throughout Edexcel A-Level Mathematics, especially in permutations, combinations and binomial expansions. Understanding how to simplify factorial expressions quickly is a core skill for both Pure and Statistics units.

阶乘记法是一种简洁地表示连续正整数乘积的方法。在 Edexcel A-Level 数学中，它广泛出现在排列、组合和二项式展开等内容中。快速化简阶乘表达式是纯数学和统计单元的核心技能。

1. Definition of Factorial Notation | 阶乘记法的定义

For a positive integer n, n! (read as “n factorial”) is the product of all positive integers from n down to 1.

对于正整数 n，n!（读作“n 的阶乘”）表示从 n 一直乘到 1 的所有正整数的乘积。

n! = n × (n − 1) × (n − 2) × ⋯ × 3 × 2 × 1

This compact notation saves time when writing long products such as 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. Instead, we simply write 8!.

这种紧凑记法可以节省书写长乘积的时间，例如 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1，我们只需写成 8!。

For example, 5! = 5 ×

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