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

Kolten Conrad 2022-06-30 Answered
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?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Sophia Mcdowell
Answered 2022-07-01 Author has 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
Did you like this example?
Subscribe for all access
Cristopher Knox
Answered 2022-07-02 Author has 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 )
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-06-21
Find the inverse function...
So, I have the function
f ( x ) = 2 x 2 x 2 .
I tried finding the inverse function the usual way I do, but I guess I'm stuck with these degrees. So far, I've come to this form
y = 2 2 x 2 0 2 x + 1 .
When I used Wolfram Alpha Inverse Function Finder, it gave me this solution
f 1 ( x ) = log ( x x 2 + 1 ) / log ( 2 ) .
I have no idea how it god those logs, please help me :D
asked 2022-10-13
Solving for the value inside a base 10 logarithm
I have an equation of log ( d ) = ( x A ) / ( 10 n ) that I need to solve for d d. How do I "reverse" the logarithm to obtain d? I apologize if this is super easy, I just can't even figure out how to Google it!
asked 2022-11-12
Is there a simple algorithm for exponentiating large numbers to large powers?
I've been thinking about this for some days, a multiplication is a lot of sums, so:
75 × 75 = 75 + 75 + 75 + 75 + 75 + 75 + 75 + 75 + 75 times
But then, there is a simple algorithm that enable us to multiply without having to sum all those numbers. In the same way, exponentiation is repeated multiplication - but I wasn't taugth about such algorithm for exponentiation. I've been thinking in representing the number with a polynomial, for example:
1038 = 10 3 + 3 10 1 + 8 10 0
Then:
1038 1038 = ( 10 3 + 3 10 1 + 8 10 0 ) 1038
But from here (considering what I currently know) I'd have to multiply it 1038 times. The mentioned multiplication would be:
( 10 3 + 3 10 1 + 8 10 0 ) 1038 = ( 10 3 + 3 10 1 + 8 10 0 ) ( 10 3 + 3 10 1 + 8 10 0 ) 1038 times
The first idea I had: There might be some connection with the binomial theorem, but I don't see how it fits. The second idea would be to find a way to write:
( 10 3 + 3 10 1 + 8 10 0 ) 1038
In which the red exponents are multiplied in some way by 1038. There might be some connection with logarithms here, but I don't see it. And it could be the case that these techniques won't yield the results I'm looking for, so: Is there a simple algorithm for large numbers elevated to large exponents?
asked 2022-10-22
Logarithmic differentiation trouble with bottom of fraction
y = ( 2 x + 3 ) 9 x ( x 2 x ) 6
I switched it to ln ( y ) = 9 ln ( 2 x + 3 ) 6 x 1 / 2 ln ( x 2 x ) and then used the log rules for derivatives I know and the product rule on the right side and wound up with
y = y [ 18 2 x + 3 3 ln ( x 2 x ) x 1 / 2 + 6 x 1 / 2 ( 2 x 1 ) x 2 x ]
The 18 2 x + 3 is the correct form but the rest is way off from the form my answer is supposed to be in. I'm not quite sure what else to do with it though...
asked 2022-06-20
Logarithm / exponential equation, not sure what to make of this, (simple)
Solve for a : ( 2 log a x ) ( 3 log x 2 4 ) = 3
No idea how to approach this problem other than moving the 2 and the 3 into an exponent..
asked 2022-10-16
Evaluate the limit lim x 0 z x ln ( z x ) x ln x
Title says it all. How can I evaluate the limit provided as:
lim x 0 + z x ln ( z x ) x ln x
I do know that it is equal to z. What I do not know is why.
asked 2021-11-08
Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.
logax+loga(x2)=loga(x+4)