Dividing factorials I'm told that <mstyle displaystyle="true" scriptlevel="0">

Kolten Conrad

Kolten Conrad

Answered question

2022-06-30

Dividing factorials
I'm told that ( n + 1 ) ! ( n + 2 ) ! simplifies to 1 n + 2 , but I dont understand how this works.
Could someone explain the theory of how to divide factorials like this?

Answer & Explanation

Sophia Mcdowell

Sophia Mcdowell

Beginner2022-07-01Added 14 answers

HINT:
Example, set n = 5
( 5 + 1 ) ! ( 5 + 2 ) ! = 6 ! 7 ! = 6 5 4 3 2 1 7 6 5 4 3 2 1 = 1 7 6 5 4 3 2 1 6 5 4 3 2 1 = 1 7 1 = 1 7 = 1 5 + 2
Cristopher Knox

Cristopher Knox

Beginner2022-07-02Added 6 answers

For an algebraic proof:
( n + 1 ) ! ( n + 2 ) ! = ( n + 1 ) n ( n 1 ) ( n 2 ) ( n 3 ) ( n 4 ) 5 4 3 2 1 ( n + 2 ) ( n + 1 ) n ( n 1 ) ( n 2 ) ( n 3 ) ( n 4 ) 5 4 3 2 1 = ( n + 1 ) n ( n 1 ) ( n 2 ) ( n 3 ) ( n 4 ) 5 4 3 2 1 ( n + 2 ) ( n + 1 ) n ( n 1 ) ( n 2 ) ( n 3 ) ( n 4 ) 5 4 3 2 1 = 1 ( n + 2 )

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