Factorial Equation Problem

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
maroonblazer
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Factorial Equation Problem

Postby maroonblazer » Sun Jul 24, 2011 4:45 am

I'm struggling to solve for x in the following:



Do I multiply each side by

Thanks in advance,
mb
Last edited by maroonblazer on Sun Jul 24, 2011 1:49 pm, edited 1 time in total.

nona.m.nona
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Re: Factorial Equation Problem

Postby nona.m.nona » Sun Jul 24, 2011 11:29 am

maroonblazer wrote:

Do I multiply each side by

You could do that, or multiply through by the larger denominator in order to get a linear equation.

Do the brackets indicate the "floor" or "ceiling" function, or something else? Thank you.

maroonblazer
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Re: Factorial Equation Problem

Postby maroonblazer » Sun Jul 24, 2011 2:04 pm

maroonblazer wrote:You could do that, or multiply through by the larger denominator in order to get a linear equation.


Thanks for your reply! I was using the brackets to separate the factorials. I've edited the question so it's clearer.

So following that approach I get:





...I've done something wrong by this point because the answer is supposed to be 15 and this isn't headed in that direction.

Help?

nona.m.nona
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Re: Factorial Equation Problem

Postby nona.m.nona » Sun Jul 24, 2011 9:44 pm

maroonblazer wrote:...I've done something wrong by this point because the answer is supposed to be 15 and this isn't headed in that direction.

My apologies: For factorials, of course (x - 7)! is larger than (x - 8)!, because (x - 7)! = 1*2*3*...*(x - 9)*(x - 8)*(x - 7), while (x - 8)! = 1*2*3*...*(x - 9)(x - 8).

Start from your first equation in your last post, noting that (x - 8)! / (x - 7)! = 1/(x - 7).

maroonblazer
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Re: Factorial Equation Problem

Postby maroonblazer » Mon Jul 25, 2011 1:21 am

nona.m.nona wrote:
maroonblazer wrote:...I've done something wrong by this point because the answer is supposed to be 15 and this isn't headed in that direction.

My apologies: For factorials, of course (x - 7)! is larger than (x - 8)!, because (x - 7)! = 1*2*3*...*(x - 9)*(x - 8)*(x - 7), while (x - 8)! = 1*2*3*...*(x - 9)(x - 8).

Start from your first equation in your last post, noting that (x - 8)! / (x - 7)! = 1/(x - 7).


Got it! Thanks very much!! :popcorn:


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