Factorial Series
Factorial Series problems consist of factorial numbers: 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720... These problems test knowledge of factorial values and ability to recognize factorial patterns.
What You'll Learn
Introduction to Factorial Series
Factorial Series problems consist of factorial numbers: 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720... These problems test knowledge of factorial values and ability to recognize factorial patterns.
Prerequisites
How to Solve Factorial Series Problems
Step 1: List factorial values: 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720
Step 2: Compare given sequence with factorial values
Step 3: Identify pattern (consecutive factorials, factorials with offsets, etc.)
Step 4: For next term: find the next factorial value
Step 5: Verify that all terms follow the factorial pattern
Step 6: Present the next term
Example Problem
Example: Find the next term: 1, 2, 6, 24, ___ Solution: Step 1: Factorials: 1!=1, 2!=2, 3!=6, 4!=24 Step 2: Pattern: n! for n=1,2,3,4 Step 3: Next term = 5! = 120 Answer: 120
Pro Tips & Tricks
- 0! = 1 (special case)
- 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720
- 7! = 5040, 8! = 40320, 9! = 362880, 10! = 3628800
- Factorial grows very fast - answer will be large for n ≥ 5
- Variation: n! + 1, n! - 1, (n+1)!, (n-1)!
- Pattern may be aₙ = n! × k (multiply by constant)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Factorial Series. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Factorial Series is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Factorial Series?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: