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Factorials C2

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    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
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    You need to express 8 x 7! as a factorial?

    The answer is 8!
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    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
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    (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


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    (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

    n^2-1
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    (Original post by steve2005)

    I hope this is want you want


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    Apologies for not being clear, they were two separate questions. Thanks for the input though.
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    (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)
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    (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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