Prove that the coefficients of `x^n` in `(1+x)^(2n)` is twice the coefficient of `x^n` in `(1+x)^(2n-1)dot`

Explanation

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

### Step 1: Identify the Coefficient in \((1+x)^{2n}\)
The coefficient of \(x^n\) in the expansion of \((1+x)^{2n}\) can be found using the binomial theorem. According to the binomial theorem, the general term \(T_{r+1}\) in the expansion of \((1+x)^m\) is given by:

\[ T_{r+1} = \binom{m}{r} x^r \]
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