$ \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.
$ \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.
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.