1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Binomial Theorem(Approximation)

  1. Aug 10, 2008 #1
    1. The problem statement, all variables and given/known data

    If p is nearly equal to q and n>1, show that [tex]\frac{(n+1)p+(n-1)q}{(n-1)p+(n+1)q}=(\frac{p}{q})^{\frac{1}{n}}[/tex]
    Note: the index 1/n is on the whole fraction (p/q)

    I think it might be helpful if I specify th chapter from which I got this question. Its the binomial thorem for indexes other than the one which are postive integral.

    2. Relevant equations

    I wonder if this needs to be used:

    when |x|<<1

    3. The attempt at a solution

    Solving L.H.S.




    as p tends to q, p-q should be a very small number (which might help me in the approximation)
    Can the fraction aded to x be converted to the format mentioned in the relevant equations?
    Or is there any other way out??
  2. jcsd
  3. Aug 10, 2008 #2
    Another way to think about the question which I thought makes things simpler:

    can be written as:


    this generated another format:

    Multiplying numerator and denominator by A+B

    and neglecting the square terms of (p-q), I get


    Can [tex]\frac{2(p-q)}{(p+q)}[/tex] be proved approximately equal to (p/q)???
  4. Aug 10, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    Hi ritwik06! :smile:

    I haven't worked this out, so I don't know that it works, but I would think that the clue " p is nearly equal to q" means that you should start by saying

    "Let q = p(1 + k) where k << 1"

    Does that help? :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook