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Math Help - Factorials & Other Stuff

  1. #1
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    Unhappy Factorials & Other Stuff

    Hi there, I need some help with these questions please:
    _______________________________________

    Find the first 5 terms of the sequence:

    tn=2^tn-1, t1=0 (I think I know this one, I just need some confirmation)

    Evaluate each of these expressions:

    12!
    ----
    5!3!

    9!
    ---- x21
    6!3!

    Simplify these expressions:

    (nē+5n+6)(n+1)!

    and

    (n+1)!
    ------
    nē+n

    Solve for n:

    3n(n!)=60n(n-2)!
    _______________________________________

    Thanks a lot. Oh, and where I put -----, it means divided by, just in case that wasn't clear.
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  2. #2
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    Quote Originally Posted by StackFryer View Post
    Hi there, I need some help with these questions please:
    _______________________________________

    Find the first 5 terms of the sequence:

    tn=2^tn-1, t1=0 (I think I know this one, I just need some confirmation)
    Looks like,
    0,1,2,4,16,...
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  3. #3
    Global Moderator

    Joined
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    New York City
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    The site is under repair thus the equation editor (LaTeX) is not avaliable. You will need to understand this mess.
    Quote Originally Posted by StackFryer View Post

    12!
    ----
    5!3!
    Expand it
    12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
    ---------------------------------------------------
    5 x 4 x 3 x 2 x 1 x 3 x 2 x 1

    What are you left with?
    12 x 11 x 10 x 9 x 8 x 7

    9!
    ---- x21
    6!3!
    Same thing.
    9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
    ----------------------------------- x 21
    6 x 5 x 4 x 3 x 2 x 1 x 3 x 2 x 1

    What are you left with?
    2 x 8 x 7 x 21


    Simplify these expressions:

    (n²+5n+6)(n+1)!
    Factor,
    (n+2)(n+3)(n+1)!
    By the definition of factorial this is,
    (n+3)!

    (n+1)!
    ------
    n²+n
    Factor the numerator and denominator as,
    (n+1)n(n-1)!
    --------------
    n(n+1)

    Thus you get,
    (n-1)!




    3n(n!)=60n(n-2)!
    Divide by 3n both sides,
    n! = 20 (n-2)!
    Express right hand side as,
    n(n-1)(n-2)!=20(n-2)!
    Divide out thus,
    n(n-1)=20
    Thus,
    n^2-n=20
    Thus,
    n^2-n-20=0
    Thus,
    (n-5)(n+4)=0
    Thus,
    n=5 or n=-4
    But!
    Factorial cannot be negative
    Thus,
    n=5
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  4. #4
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    Thanks a lot, I really appreciate it.
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