Find the sum of coefficients in `(1+x-3x^2)^(4163)`.

Explanation

To find the sum of coefficients in the expression \( (1 + x - 3x^2)^{4163} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Sum of Coefficients**:
The sum of the coefficients in a polynomial can be found by substituting \( x = 1 \) into the polynomial. This is because substituting \( x = 1 \) effectively adds up all the coefficients.

2. **Substituting \( x = 1 \)**:
We substitute \( x = 1 \) into the expression:
\[ (1 + 1 - 3(1)^2)^{4163} \]

3. **Simplifying the Expression**:
Now, simplify the expression inside the parentheses:
\[ 1 + 1 - 3(1) = 1 + 1 - 3 = 2 - 3 = -1 \]

4. **Raising to the Power**:
Now we raise the result to the power of 4163:
\[ (-1)^{4163} \]

5. **Determining the Result**:
Since 4163 is an odd number, we know that:
\[ (-1)^{4163} = -1 \]

6. **Final Answer**:
Therefore, the sum of the coefficients in the expression \( (1 + x - 3x^2)^{4163} \) is:
\[ \boxed{-1} \]