lehaley4776 lehaley4776
  • 02-05-2021
  • Mathematics
contestada

Find the value of n that satisfies 2(n+1)! + 6n! = 3(n+1), where $n! = n\cdot (n-1)\cdot (n-2) \cdots 2\cdot 1$.

Respuesta :

MrRoyal
MrRoyal MrRoyal
  • 03-05-2021

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]

Answer Link

Otras preguntas

why would an asteroid have a difficult time of holding a probe or person?
What happens to the Mississippi River water when it flows into the Gulf of Mexico?
How is Europe connected
where the sun's energy is produced
what number is 6.1% of 60
In terms of ion charges and chemical change, what is the difference between CuF(s) and CuF2(s)??
Which British poet of the Romantic movement found inspiration in England's Lake District? A. Johann Wolfgang von Goethe B. William Wordsworth C. Lord Byron D. J
the newspaper reported that 134.8 million viewers watched the Super Bowl. Write the number of viewers in standard form
Who is Alexander the great?
1. Describe one major difference in human behavior before and after the Agricultural Revolution, 10,000 years ago