Factorials: (4n + 1)! / (4n - 1)!  TOPIC_SOLVED

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Factorials: (4n + 1)! / (4n - 1)!

Postby Mere on Fri Aug 07, 2009 3:04 am

Can someone explain how to do this problem, please?

(4n+1)!/(4n-1)!
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Postby stapel_eliz on Fri Aug 07, 2009 12:50 pm

Mere wrote:Can someone explain how to do this problem, please?

(4n+1)!/(4n-1)!

I'll guess that the instructions were something along the lines of "simplify"...?

To learn how factorials work, try here.

Once you're familiar with how they work, write out the expansions of the two expressions in the fraction. For instance, the numerator would expand as:

. . . . .

How would the other factorial expression expand? What will cancel out? What then will be left? :wink:
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Re: Factorials: (4n + 1)! / (4n - 1)!  TOPIC_SOLVED

Postby Mere on Fri Aug 07, 2009 5:30 pm

So then... the denominator would be: 1x2x3x(4n-2)x(4n-1)
And all of that would cancel out with the numerator, leaving (4n)x(4n+1), which is (16(n^2))+4n!

Thank you sooooo much! :clap:
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Postby stapel_eliz on Fri Aug 07, 2009 5:34 pm

Mere wrote:So then... the denominator would be: 1x2x3x(4n-2)x(4n-1)

Not quite; you need to include all the numbers in the middle which have been omitted:

. . . . .

Mere wrote:And all of that would cancel out with the numerator, leaving (4n)x(4n+1), which is (16(n^2))+4n!

Not quite: 4n(4n + 1) = 4n(4n) + 4n(1) = 16n2 + 4n, not 16n2 + (4n)!. :oops:

Make those two corrections, and I believe you've got it! :D
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Re: Factorials: (4n + 1)! / (4n - 1)!

Postby Mere on Fri Aug 07, 2009 6:01 pm

Oh! Okay. Thank you!
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