Factorial Values and Recursion

Factorial Values and Recursion

What is it?

1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.

In simple words

• 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
• 6! = 6*5!
• 10! huge
• State the rule, show the working, and check the answer.

Important terms

FACTORIAL VALUES AND RECURSION: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.

VALUES: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.

What you should learn

• State the rule or meaning of factorial values and recursion in easy words.
• Apply factorial values and recursion in a clear step-by-step solution.
• Check the conditions, working, and final answer for accuracy.

Examples

• 6! = 6*5!
• 10! huge
• 0! = 1 not 0

MAIN IDEA

1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.

EXAM USE

Write the rule first: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Full school-level explanation

1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.

Understand the idea, then apply it:

WHAT — FACTORIAL VALUES AND RECURSION

1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.

WHY — Why it matters

This rule is a separate learning unit inside factorial n!. It can be defined, applied, and checked in its own FBISE question.

HOW — How to answer

Write the rule first: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

MAIN IDEA

1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.

Remember

• build from smaller

Examples

• 6! = 6*5!
• 10! huge
• 0! = 1 not 0

EXAM USE

Write the rule first: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Remember

• focused answer
• accurate support

Examples

• State the central idea
• Use one accurate detail
• Check the final response

How to answer a factorial values and recursion question

How it works

• Read the exact command word and identify what the question asks.
• State the matching idea, rule, or meaning before adding detail.
• Use the unit evidence or mathematical working that directly supports the answer.
• Check accuracy, relevance, and answer length before finishing.

Remember

• build from smaller
• n! = 12...*n
• 0! = 1
• 0! is 1
• build from smaller
• focused answer
• accurate support
• build from smaller

Deeper understanding

Go beyond memorising Factorial Values and Recursion. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

What to Know

Example or Evidence

How to Answer

Exam focus

Quick revision

• build from smaller
• n! = 12...*n
• 0! = 1
• 0! is 1
• FACTORIAL VALUES AND RECURSION: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper
• VALUES: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.

0! = 1. If you put 0, nCr formulas break at r=0.

For long answers on Factorial Values and Recursion: define clearly → explain the main parts → give one example → state one exam caution.