Show that , if the greatest term in the expansion of `(1 + x)^(2n)` has also the greatest coefficient
then x lies between `(n)/(n +1) " and" (n+1)/(n)`

Explanation

To solve the problem, we need to show that if the greatest term in the expansion of \( (1 + x)^{2n} \) also has the greatest coefficient, then \( x \) lies between \( \frac{n}{n + 1} \) and \( \frac{n + 1}{n} \).

### Step 1: Identify the General Term
The general term \( T_r \) in the expansion of \( (1 + x)^{2n} \) is given by:
\[ T_r = \binom{2n}{r} x^r \]
where \( r = 0, 1, 2, \ldots, 2n \).
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