Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    heyy,
    can anyone help me on this qs please :
    in the binomial expression of (2k + x) ^ n where k is a constant and n is a positive integer, the coefficient of x^2 is equal to the coefficient of x^3
    prove n = 6k + 2

    so heres what i got up to (not far!)...i apologise in advance if its not very clear

    (n/2) (2k) ^ (n-2) x^2 = (n/3) (2k) ^ n-3 x^3


    thanks
    • PS Helper
    Offline

    14
    PS Helper
    I take it by n/2 and n/3 you mean the binomial coefficients \binom{n}{2} and \binom{n}{3}?

    Basically, you're on the right lines, but your equation shouldn't have the x bits in there (it's the coefficient, not the whole term). A good first step would be to put the binomial coefficients in terms of factorials; a lot of things will cancel out.

    Basically you have
    \dfrac{n!}{2!(n-2)!} (2k)^{n-2} = \dfrac{n!}{3!(n-3)!}(2k)^{n-3}
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    I take it by n/2 and n/3 you mean the binomial coefficients \binom{n}{2} and \binom{n}{3}?

    Basically, you're on the right lines, but your equation shouldn't have the x bits in there (it's the coefficient, not the whole term). A good first step would be to put the binomial coefficients in terms of factorials; a lot of things will cancel out.

    Basically you have
    \dfrac{n!}{2!(n-2)!} (2k)^{n-2} = \dfrac{n!}{3!(n-3)!}(2k)^{n-3}

    haha yes i did mean that...dont no how to do the fancy writing on here .... why dont i put the x's in ? and ive not been taught it ur way, like we've been taught how to use the ( 1 + x) ^ n using factorials, but dont know hot to adjust this when its not 1 at the start (if that makes sense) do you know how i could still get the answer with my working minus the x's.... thankyou for your help as well
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by _anum)
    haha yes i did mean that...dont no how to do the fancy writing on here

    See http://www.thestudentroom.co.uk/wiki/LaTex
    It's well worth learning, and easy to pick up.

    .... why dont i put the x's in ?
    You don't need the x's as you are only interested in the coefficients of the terms. For example if you had ax^2 then the coefficient of x^2 is just a.

    and ive not been taught it ur way, like we've been taught how to use the ( 1 + x) ^ n using factorials, but dont know hot to adjust this when its not 1 at the start (if that makes sense)
    You may find this useful http://en.wikipedia.org/wiki/Binomial_theorem.
    If not, just try googling binomial theorem

    do you know how i could still get the answer with my working minus the x's.... thankyou for your help as well
    See Nuodai's equation, and start cancelling down. Almost everything will cancel out and the terms you are left with can be manipulated into the desired equation.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by ghostwalker)
    See http://www.thestudentroom.co.uk/wiki/LaTex
    It's well worth learning, and easy to pick up.



    You don't need the x's as you are only interested in the coefficients of the terms. For example if you had ax^2 then the coefficient of x^2 is just a.



    You may find this useful http://en.wikipedia.org/wiki/Binomial_theorem.
    If not, just try googling binomial theorem



    See Nuodai's equation, and start cancelling down. Almost everything will cancel out and the terms you are left with can be manipulated into the desired equation.

    aww thankyou so much for all that
    the whole coefficient thing has just clicked
    will try that n see if i get the answer after searching around how to do it! ...
    thanks a lot for that
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    I take it by n/2 and n/3 you mean the binomial coefficients \binom{n}{2} and \binom{n}{3}?

    Basically, you're on the right lines, but your equation shouldn't have the x bits in there (it's the coefficient, not the whole term). A good first step would be to put the binomial coefficients in terms of factorials; a lot of things will cancel out.

    Basically you have
    \dfrac{n!}{2!(n-2)!} (2k)^{n-2} = \dfrac{n!}{3!(n-3)!}(2k)^{n-3}

    okay now looked in my book (so ignore my last post!) and i have been taught that way( just me being stupid :rolleyes:) ... i understand how you got the equation but i still dont know how to solve it... i cant see how anything cancels out? sorry to be a pain
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by _anum)
    okay now looked in my book (so ignore my last post!) and i have been taught that way( just me being stupid :rolleyes:) ... i understand how you got the equation but i still dont know how to solve it... i cant see how anything cancels out? sorry to be a pain
    I find that hard to believe. Have a think about it. Don't be overwhelmed by what you see; look at the detail.


    1) What "bits" are the same on each side?


    2) The (2k) terms are related in a structure similar to:

      ax^n= bx^{n+1}

    You should know how to solve that sort of equation?

    3) How do you expand a factorial? Or what's, for example n!/(n-1)!
    • Thread Starter
    Offline

    0
    ReputationRep:
    okay..... thankyou for your help
 
 
 
The home of Results and Clearing

1,246

people online now

1,567,000

students helped last year

University open days

  1. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
  2. University of Glasgow
    All Subjects Undergraduate
    Tue, 28 Aug '18
  3. University of Aberdeen
    Undergraduate Open Day Undergraduate
    Tue, 28 Aug '18
Poll
How are you feeling about GCSE results day?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.