Calculating (n+2)! quickly and accurately - Help Needed!

  • Thread starter Phyzwizz
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    Factorial
In summary, to find (n+2)! and its quotient with n!, you can use the expansion of n! and add 1 to n to find the additional term in (n+2)!, which is (n+2)(n+1). This means that the quotient of (n+2)!/n! is (n+2)(n+1).
  • #1
Phyzwizz
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I know that n!=(1)(2)(3)...(n-1)(n)
I am confused how I can figure out what (n+2)! is in order to divide it by n!
How can I figure (n+2)! out and what is it, so that I won't have to ask if what I got is right.

Thanks!
 
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  • #2
You have already written out the expansion for n!. Now, if you add 1 to n, what additional term must be included in n! to make it (n+1)! Once you figure this out, repeat to find
(n+2)!
 
  • #3
3!=3*2*1
4!=4*3*2*1
10!=10*9*8*...*2*1
etc.
What is 10! divided by 8! then?
 
  • #4
oh okay so (n+2)! would be (1)(2)(3)...(n-1)(n)(n+1)(n+2)?
 
  • #5
Right. Now figure your quotient (n+2)!/n!.
 
  • #6
Phyzwizz said:
oh okay so (n+2)! would be (1)(2)(3)...(n-1)(n)(n+1)(n+2)?
Which is the same as (n + 2)(n + 1) n!, right?
 
  • #7
There is no n! in the quotient of (n+2)!/n!. Remember the expansion of (n+2)! is
(n+2)(n+1)n!. Dividing (n+2)! by n! is (n+2)(n+1)n!/n! = (n+2)(n+1).
 

1. How do I calculate (n+2)! quickly and accurately?

To calculate (n+2)! quickly and accurately, you can use a mathematical formula or a calculator. Alternatively, you can break down the equation into smaller parts and simplify them to make the calculation easier.

2. What is the purpose of calculating (n+2)!?

(n+2)! is the factorial of n+2, which is used in various mathematical equations and models. It represents the number of ways in which n+2 objects can be arranged in a specific order.

3. Can I use any value for n when calculating (n+2)!?

Yes, you can use any positive integer value for n when calculating (n+2)!. However, as n increases, the number of calculations required also increases, making it more challenging to calculate quickly and accurately.

4. Are there any shortcuts or tips for calculating (n+2)!?

Yes, there are several shortcuts and tips that can help you calculate (n+2)! quickly and accurately. These include using mathematical identities, breaking down the equation into smaller parts, and using a calculator or computer program.

5. Is there a specific order in which the calculations for (n+2)! should be performed?

No, there is no specific order in which the calculations for (n+2)! should be performed. As long as you follow the correct mathematical formula and use accurate values for n, you will get the same result regardless of the order in which you perform the calculations.

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