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Feinsn

Feinsn

Answered question

2022-06-21

Show that ( n + 2 ) ! + ( n + 1 ) ! + n ! ?

Answer & Explanation

Mateo Barajas

Mateo Barajas

Beginner2022-06-22Added 13 answers

Step 1
Start with the expression on the left:
( n + 2 ) !
Simplify using factorials:
( n + 2 ) ( n + 1 ) n ! + ( n + 1 ) n ! + n !
Factor out the n!:
n ! ( ( n + 2 ) ( n + 1 ) + ( n + 1 ) + 1 )
Step 2
Simplify inside the parentheses:
n ! ( n 2 + 3 n + 2 + n + 2 )
n ! ( n 2 + 4 n + 4 )
Factor:
n ! ( n + 2 ) 2
So: ( n + 2 ) !

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