Can someone explain how to do this problem, please?

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

Can someone explain how to do this problem, please?

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

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

- stapel_eliz
**Posts:**1687**Joined:**Mon Dec 08, 2008 4:22 pm-
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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

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?

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!

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!

- stapel_eliz
**Posts:**1687**Joined:**Mon Dec 08, 2008 4:22 pm-
**Contact:**

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) = 16n

Make those two corrections, and I believe you've got it!

Oh! Okay. Thank you!