1
$\begingroup$

$ \qquad \qquad $ The greatest term in $\left(1+x\right)^{2n}$ has the greatest cofficient if $\frac{n}{n+1} \lt x \lt \frac{n+1}{n}$


Can we derive something like this for $n$ in general? Please give me some hints.

  • 0
    There is an article about the greatest term which might help (scroll down to the relevant section on the greatest term) http://www.tutors4you.com/binomialtheoremtutorial.htm2010-12-12

1 Answers 1

4

Hint: I think you can solve this by looking at the adjacent terms of the middle term. If the middle term is the biggest term, it has to be bigger than both adjacent terms. This will give you the bounds.