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# What does n! mean

In the algebra problem: for any positive integers n,(n+1)!/n! -n=0 what does the ! mean?

### 4 Answers by Expert Tutors

Miles A. | An enthusiastic game designer with experience teaching childrenAn enthusiastic game designer with exper...
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The ! in n! means n-factorial. A factorial is the product of all positive integers less than n.

Matthew S. | Statistics, Algebra, Math, Computer Programming TutorStatistics, Algebra, Math, Computer Prog...
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n! refers to a factorial, a product of n numbers, each one less than the preceding value. You can write a factorial n! by starting with the number n, multiplying it by one less than the previous number, and repeat until you reach 1, at which time you can stop. So 5! can be written as follows: 5! = 5 * 4 * 3 * 2 * 1 = 120. Similarly, 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720. Note all the repetition here... it turns out 6! = 6 * 5! That's important because you can re-write (n+1)! as (n+1) * n! So when you divide (n+1)! by n! as you have in the first term, the n! cancels out in both numerator and denominator leaving only (n+1). So as Robert points out, subtracting n from the first term would leave 1, not 0. So it appears the second term should be (n+1) to be valid.
Edgardo O. | Math, ballroom dancing and ki ho' alu tutoring available. Math, ballroom dancing and ki ho' alu tu...
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The ! is the factorial sign.  Example 4! = 4 x 3 x 2 x 1

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
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(n+1)!/n! -n ≠ 0

Do you mean (n+1)!/n! - (n+1) = 0?

Since (n+1)!/n!  = (n+1)n!/n! = n+1, (n+1)!/n! - (n+1) = 0 is an identity for any positive integers n.