Answer:
[tex]n = 5[/tex]
Step-by-step explanation:
Given
[tex]2(n+1)! + 6n! = 3(n+1)![/tex]
Required
Find n
Simplify (n + 1)!
[tex]2(n+1)*n! + 6n! = 3(n+1)*n![/tex]
Factorize
[tex]n![2(n+1) + 6] = 3(n+1)*n![/tex]
Divide both sides by n!
[tex]2(n+1) + 6 = 3(n+1)[/tex]
Open brackets
[tex]2n + 2 + 6 = 3n + 3[/tex]
[tex]2n + 8 = 3n + 3[/tex]
Collect like terms
[tex]2n - 3n = 3 -8[/tex]
[tex]-n =-5[/tex]
Multiply both sides by -1
[tex]n = 5[/tex]
