Prove that the coefficient of `x^(n)` in the binomial expansion of `(1+x)^(2n)` is twice the coefficient of `x^(n)` in the binomial expansion of `(1+x)^(2n-1)`.

Explanation

To prove that the coefficient of \( x^n \) in the binomial expansion of \( (1+x)^{2n} \) is twice the coefficient of \( x^n \) in the binomial expansion of \( (1+x)^{2n-1} \), we will follow these steps:

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

The general term in the binomial expansion of \( (1+x)^{2n} \) is given by:

\[
T_{r+1} = \binom{2n}{r} x^r
...