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:**1628**Joined:**Mon Dec 08, 2008 4:22 pm-
**Contact:**

I'll guess that the instructions were something along the lines of "simplify"...?Can someone explain how to do this problem, please?

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

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:**1628**Joined:**Mon Dec 08, 2008 4:22 pm-
**Contact:**

Not quite; you need to include all the numbers in the middle which have been omitted:So then... the denominator would be: 1x2x3x(4n-2)x(4n-1)

. . . . .

Not quite: 4n(4n + 1) = 4n(4n) + 4n(1) = 16nAnd all of that would cancel out with the numerator, leaving (4n)x(4n+1), which is (16(n^2))+4n!

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

Oh! Okay. Thank you!