The series $2 - 4 + 8 - 16 + 32 - \ldots + 1024$ can be expressed using summation notation as follows:

$\sum_{n=1}^{10} (-1)^{n+1} \cdot 2^n$

Here, $n$ starts from 1 and goes up to 10, where $2^n$ represents the terms of the series. The factor $(-1)^{n+1}$ alternates the signs.

If you have any questions or need further details, feel free to ask! Here are some related questions to consider:

1. How do you derive the general term of the series?
2. What is the sum of the series using this notation?
3. Can this series be represented as a geometric series?
4. How would you evaluate the sum of this series?
5. What is the convergence behavior of similar series?

Tip: To calculate the sum of alternating series, consider grouping the terms in pairs for simplification.