Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Please help me with difficult binomial expansion mathematics -10 points?
If the first three terms in the expansion of (1+kx)^n in ascending powers of x are 1-6x + (33x^2)/2. Find the value of k and n
Please include working out and step by step method.
Also, please answer my other binomial expansion questions
Thanks! Ill award 10 points to do the best question
1 Answer
- 9 years agoFavorite Answer
okay - so..
the first 3 terms of the expansion are
1 + (nC1)kx + (nC2)(kx)^2 we know (nC1) is n so we get
nk = -6 and n!/2!(n-2)! k^2 = 33/2
k = -6/n subt in to get n!/2!(n-2)!*(-6/n)^2 = 33/2
=> n!/2!(n-2)!*(36/n^2) = 33/2
=> 36 * n* (n-1)! / (2 * n^2 * (n-2)!) = 33/2 note (n-1)! / (n-2)! = (n-1)
=> 36(n-1) / 2n = 33/2
=> (n-1)/n = 33/36
=> (n-1)/n = 11/12
=> n = 12 and as nk = -6, k=-1/2