If `(1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2)`
` + C_(3) x^(3) + C_(4) x^(4) + ...,` find the values of
(i) `C_(0) - C_(2) + C_(4) - C_(0) + …`
(ii) `C_(1) - C_(3) + C_(5) - C_(7) + …`
(iii) `C_(0) + C_(3) + C_(6) + …`

Explanation

To solve the problem, we need to find the values of three different series based on the binomial expansion of \((1 + x)^n\). The coefficients in the expansion are denoted as \(C_k\), where \(C_k = \binom{n}{k}\).

### Step-by-step Solution:

1. **Understanding the Binomial Expansion**:
The binomial expansion of \((1 + x)^n\) is given by:
\[
(1 + x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + C_4 x^4 + \ldots
...