# The interval in which $x$ must lie so that the greatest term in the expansion of $(1+x)^{2n}$, ($x>0$) has greatest coefficient is

$\begin{array}{1 1} \bigg(\large\frac{n-1}{n},\frac{n}{n-1}\bigg) \\\bigg(\large\frac{n}{n+1},\frac{n+1}{n}\bigg) \\\bigg(\large\frac{n}{n+2},\frac{n+2}{n}\bigg) \\ \bigg(\large\frac{n-1}{n+1},\frac{n+1}{n-1}\bigg) \end{array}$

<div class="clay6-step-odd"><div class="clay6-basic" id="pr10">The greatest term in $(1+x)^{2n}$ has the greatest coefficient if \begin{align*} \frac{n}{n+1} &lt; x &lt; \frac{n+1}{n} \end{align*}</div><div class="clay6-basic" id="pr11">$\bigg(\large\frac{n}{n+1},\frac{n+1}{n}\bigg)$</div></div>
edited Dec 4, 2017