To find the sum of the given numbers, you simply add them together:

$17 + 9 + 8 + 14 + 13 + 25 + 1 + 12 + 5 + 6$

Let's add these step-by-step:

$17 + 9 = 26$

$26 + 8 = 34$

$34 + 14 = 48$

$48 + 13 = 61$

$61 + 25 = 86$

$86 + 1 = 87$

$87 + 12 = 99$

$99 + 5 = 104$

$104 + 6 = 110$

So, the total sum is:

$17 + 9 + 8 + 14 + 13 + 25 + 1 + 12 + 5 + 6 = 110$

Would you like more details or have any questions? Here are some related questions that might interest you:

1. How do you find the average of a set of numbers?
2. What are some common techniques for adding a series of numbers quickly?
3. How can you check if your addition is correct?
4. What is the difference between addition and multiplication when dealing with series of numbers?
5. How do you handle addition of negative numbers?
6. What is the sum of the first 10 positive integers?
7. How do you add numbers with different units (like meters and centimeters)?
8. Can you provide an example of addition in a real-life scenario?

Tip: When adding a series of numbers, it's often helpful to group them into pairs or sets that make round numbers (like 10, 20, etc.) to simplify the addition process.