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Factorials C2

Hi all, I'm working on sequences today however my textbook is not very clear on the topic of factorials. It gives very few examples. I am currently working through the questions at the end of the section but I am confused with the following:

Express as a factorial:

n(n^2-1)
8x7!

Apologies is these are very basic questions but the book only gives basic examples and explanation e.g. 8!/7!

If you could explain to me how I should approach Q's like that it would be much appreciated
Reply 1
Avatar for TenOfThem
TenOfThem
18
You need to express 8 x 7! as a factorial?

The answer is 8!
Reply 2
Avatar for vinvinvin
vinvinvin
OP
4
Ok I get that, 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 but how do I approach the other Q:

n(n^2-1) as a factorial
Reply 3
Avatar for steve2005
steve2005
17
Original post by vinvinvin
Hi all, I'm working on sequences today however my textbook is not very clear on the topic of factorials. It gives very few examples. I am currently working through the questions at the end of the section but I am confused with the following:

Express as a factorial:

n(n^2-1)
8x7!

Apologies is these are very basic questions but the book only gives basic examples and explanation e.g. 8!/7!

If you could explain to me how I should approach Q's like that it would be much appreciated



I hope this is want you want


Uploaded with ImageShack.us
Reply 4
Avatar for TenOfThem
TenOfThem
18
Original post by vinvinvin
Ok I get that, 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 but how do I approach the other Q:

n(n^2-1) as a factorial


Factorise

n2−1n^2-1
Reply 5
Avatar for vinvinvin
vinvinvin
OP
4
Original post by steve2005

I hope this is want you want


Uploaded with ImageShack.us


Apologies for not being clear, they were two separate questions. Thanks for the input though.
Reply 6
Avatar for The Mr Z
The Mr Z
13
Original post by vinvinvin
Hi all, I'm working on sequences today however my textbook is not very clear on the topic of factorials. It gives very few examples. I am currently working through the questions at the end of the section but I am confused with the following:

Express as a factorial:

n(n^2-1)
8x7!

Apologies is these are very basic questions but the book only gives basic examples and explanation e.g. 8!/7!

If you could explain to me how I should approach Q's like that it would be much appreciated


The key is to recognise what a factorial is - it is simply the multiplicative equivalent of a series summation.

i.e. n! = 1x2x3x4x...x(n-1)xn

you multiply all the numbers from 1 to n (inclusive) together.

so to do 8 x 7!

7! = 1x2x3x4x5x6x7
multiply by 8
1x2x3x4x5x6x7x8

which is, just by looking at it, 8!

equally, if you want to do a!/b!, with b<a,
a! = 1x2x...xbx(b+1)...xa
b! = 1x2x...xb

cancelling all the terms that match leaves only (b+1)x(b+2)x....xa

for n(n^2-1)

recognise using difference of two squares that (n^2-1) = (n+1)x(n-1)
so you want to express (n-1) x n x (n+1) in factorial terms (find suitable a and b such that a!/b! gives this)
Reply 7
Avatar for vinvinvin
vinvinvin
OP
4
Original post by The Mr Z
The key is to recognise what a factorial is - it is simply the multiplicative equivalent of a series summation.

i.e. n! = 1x2x3x4x...x(n-1)xn

you multiply all the numbers from 1 to n (inclusive) together.

so to do 8 x 7!

7! = 1x2x3x4x5x6x7
multiply by 8
1x2x3x4x5x6x7x8

which is, just by looking at it, 8!

equally, if you want to do a!/b!, with b<a,
a! = 1x2x...xbx(b+1)...xa
b! = 1x2x...xb

cancelling all the terms that match leaves only (b+1)x(b+2)x....xa

for n(n^2-1)

recognise using difference of two squares that (n^2-1) = (n+1)x(n-1)
so you want to express (n-1) x n x (n+1) in factorial terms (find suitable a and b such that a!/b! gives this)


That is a fantastic help thank you, it's all clear now.

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