$\begin{array}{c}4-2+1-\frac{1}{2}+\cdots-\frac{1}{8} \\ 436\end{array}$

Step 1 ：\(\text{integer_sum} = 4 - 2 + 1 = 3\)

Step 2 ：\(\text{fraction_sum} = -\frac{1}{2} + \frac{1}{4} - \frac{1}{8} = -0.375\)

Step 3 ：\(\text{total_sum} = \text{integer_sum} + \text{fraction_sum} = 3 + (-0.375) = 2.625\)

Step 4 ：\(\boxed{\text{Final Answer: The sum of the given series is 2.625}}\)