Let's solve each of the expressions step by step.

### Expression h:
\[
2024 - 2023 + 2021 - 2020 + ... + 4 - 3 + 2 - 1
\]

This series alternates between subtracting and adding consecutive numbers. We can group them in pairs:

\[
(2024 - 2023) + (2021 - 2020) + ... + (4 - 3) + 2 - 1
\]

Calculating the paired terms:

- Each pair (n - (n-1)) equals 1.
- The number of complete pairs from 2024 to 1 is \(1012\) (the sequence has \(2024\) terms, half of which can be paired).
- The remaining terms are \(2 - 1\).

Thus, we can express this as:
\[
1012 + 1 = 1013
\]

### Expression i:
\[
2016 + 2015 - 2014 - 2013 + 2012 + 2011 - 2010 - 2009 + ... + 4 + 3 - 2 - 1
\]

For this, we can group it into sets of four:

\[
(2016 + 2015 - 2014 - 2013) + (2012 + 2011 - 2010 - 2009) + ... + (4 + 3 - 2 - 1)
\]

Calculating one set:
\[
(2016 + 2015) - (2014 + 2013) = 4031 - 4027 = 4
\]

The sequence continues down to \(4, 3, 2, 1\) forming 505 groups.

Calculating:
\[
505 \times 4 = 2020
\]

So the sum is:
\[
2020
\]

### Expression j:
\[
1 - 5 + 9 - 13 + 17 - 21 + 25 - ... + 2001 - 2005 - 2009 + 2013
\]

This sequence consists of alternating sums and subtractions of an arithmetic sequence of odd numbers. Split into pairs:

\[
(1 - 5) + (9 - 13) + (17 - 21) + ... + (2001 - 2005) + 2013
\]

Each pair calculates to \(-4\):
- Each odd-pair ultimately simplifies:
\[
-4 \text{ (for each complete pair)}
\]

To find the number of complete pairs:
- This sequence ends at 2013, capturing pairs from 1 to 2005 (999 total odd numbers).
- Total pairs = \(999 / 2 \approx 499\) full pairs (the last term remains 2013).

The total:
\[
499 \times (-4) + 2013
\]
This gives:
\[
-1996 + 2013 = 17
\]

### Final Results:
- h) \(1013\)
- i) \(2020\)
- j) \(17\)