Notasi Faktorial Kelas 12 - Nyatakan dalam Notasi Faktorial

Summary

In this video, the presenter explains the concept of factorial notation, essential for understanding permutations and combinations. The video covers the basic definition of factorial, how to calculate factorials for numbers like 5 and 2, and provides examples of using factorials in division and sequential multiplication problems. The presenter also demonstrates how to simplify complex factorial expressions and solve equations involving factorials. The video concludes with practice problems, encouraging viewers to apply the concepts to enhance their understanding. The goal is to make factorial notation clear and accessible to viewers, paving the way for more advanced mathematical topics.

Takeaways

• 😀 Factorial notation is represented by an exclamation mark and involves multiplying numbers sequentially from n down to 1.
• 😀 0 factorial (0!) is defined as 1, which is an exception to the general pattern.
• 😀 To calculate a factorial, such as 5!, you multiply the number by every integer down to 1 (e.g., 5 × 4 × 3 × 2 × 1 = 120).
• 😀 Factorial calculations can be applied in addition, like in the case of 2! + 3! = 2 + 6 = 8.
• 😀 In division of factorials, common factors can be canceled out. For example, 20! ÷ 17! simplifies to 20 × 19 × 18 = 5700.
• 😀 When dividing factorials with shared factors, cancel out the common factorials to simplify the calculation.
• 😀 For expressions like 15! ÷ (14! × 1! × 2!), simplify the factorials and cancel out common terms to make the calculation easier.
• 😀 Factorial notation can represent a sequence of multiplicative steps. For example, 7 × 6 × 5 can be rewritten as 7! ÷ 4!.
• 😀 When solving for an unknown in a factorial equation, look for the consecutive numbers that fit the result (e.g., n! ÷ (n-3)! = 60 leads to n = 5).
• 😀 Another example involves finding n in a factorial equation, such as (n+1)! ÷ (n-2)! = 120, where n is determined by the multiplication of consecutive integers (6 × 5 × 4 = 120).

Q & A

What is factorial notation and how is it symbolized?

Factorial notation is represented by an exclamation mark (!), and it involves multiplying consecutive numbers starting from a given number n and decreasing until the number 1. For example, n! = n × (n-1) × (n-2) × ... × 2 × 1.

What is the factorial of 0?

The factorial of 0 is defined as 1, i.e., 0! = 1.

How do you calculate 5 factorial?

To calculate 5 factorial (5!), you multiply the consecutive numbers from 5 down to 1: 5 × 4 × 3 × 2 × 1 = 120.

What is the result of 2 factorial plus 3 factorial?

2! + 3! is calculated as follows: 2! = 2 × 1 = 2 and 3! = 3 × 2 × 1 = 6. So, 2! + 3! = 2 + 6 = 8.

How do you calculate 20 factorial divided by 17 factorial?

To calculate 20! ÷ 17!, you can simplify by cancelling out the 17! part from both the numerator and denominator, leaving you with 20 × 19 × 18, which equals 5700.

How do you solve the equation 15 factorial divided by 14 factorial times 2 factorial?

For 15! ÷ (14! × 2!), simplify the factorials: 15! = 15 × 14 × 13!, and 14! is cancelled out. The remaining equation is (15 × 14) ÷ 2!, and since 2! = 2, you get 15 × 7 = 105.

How do you convert sequential multiplication into factorial notation?

To convert sequential multiplication into factorial notation, you identify the sequence of numbers. For example, for 7 × 6 × 5, the missing numbers 4, 3, 2, 1 can be added to form 7! ÷ 4!.

How do you express the product of 14 × 13 × 12 × ... in factorial notation?

The product 14 × 13 × 12 × ... can be written as 14! ÷ 11!, where the missing numbers 11, 10, 9, etc., are represented as the factorial of 11.

How do you calculate n if n factorial divided by (n-3) factorial equals 60?

To solve n! ÷ (n-3)! = 60, you simplify the equation to n × (n-1) × (n-2) = 60. By trial, you find that n = 5, as 5 × 4 × 3 = 60.

How do you solve the equation (n+1) factorial divided by (n-2) factorial equals 120?

To solve (n+1)! ÷ (n-2)! = 120, simplify the equation to (n+1) × n × (n-1) = 120. By trial, you find that n = 5, as 6 × 5 × 4 = 120.