Find the sum of the series `^10 C_0+^(10)C_1+^(10)C_2++^(10)C_7dot`

Explanation

To find the sum of the series \( \binom{10}{0} + \binom{10}{1} + \binom{10}{2} + \binom{10}{3} + \binom{10}{4} + \binom{10}{5} + \binom{10}{6} + \binom{10}{7} \), we can use the properties of binomial coefficients.

### Step-by-step Solution:

1. **Understanding the Binomial Theorem**:
The binomial theorem states that:
\[
(1 + x)^n = \sum_{k=0}^{n} \binom{n}{k} x^k
...