What is the sum of the coefficients in the expansion of `(1+x)^(n)` ?

Options

A. `2^(n)`
B. `2^(n)-1`
C. `2^(n)+1`
D. `n+1`

Explanation

To find the sum of the coefficients in the expansion of \((1+x)^n\), we can follow these steps:

### Step 1: Understand the Binomial Expansion
The binomial theorem states that:
\[ (1+x)^n = \sum_{k=0}^{n} \binom{n}{k} x^k \]
where \(\binom{n}{k}\) is the binomial coefficient, representing the number of ways to choose \(k\) elements from \(n\).

### Step 2: Identify the Coefficients
In the expansion, the coefficients are given by \(\binom{n}{k}\) for \(k = 0, 1, 2, \ldots, n\). Thus, the sum of the coefficients in the expansion is:
\[ \binom{n}{0} + \binom{n}{1} + \binom{n}{2} + \ldots + \binom{n}{n} \]

### Step 3: Evaluate the Sum of Coefficients
To find the sum of the coefficients, we can substitute \(x = 1\) into the expansion:
\[ (1+1)^n = 2^n \]
This means that the sum of the coefficients is equal to \(2^n\).

### Conclusion
Therefore, the sum of the coefficients in the expansion of \((1+x)^n\) is:
\[ \text{Sum of coefficients} = 2^n \]