Show that the coefficient of the middle term in the expansion of `(1+x)^(2n)`is equal to the sum of the coefficients of two middle terms in the expansion of `(1+x)^(2n-1)`.

Explanation

To show that the coefficient of the middle term in the expansion of \((1+x)^{2n}\) is equal to the sum of the coefficients of the two middle terms in the expansion of \((1+x)^{2n-1}\), we will follow these steps:

### Step 1: Find the Middle Term of \((1+x)^{2n}\)

In the expansion of \((1+x)^{2n}\), the total number of terms is \(2n + 1\) (since the power is \(2n\)). The middle term is the \((n+1)\)-th term (since we start counting from 0).

The coefficient of the \((n+1)\)-th term is given by:
\[
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