The expression in the image is a summation:

$\sum_{i=1}^{10} (i^3 - 2)$

This expression means we will evaluate $i^3 - 2$ for each integer $i$ from 1 to 10 and then sum all the results.

Step-by-Step Calculation:

1. Calculate $i^3 - 2$ for each $i$ from 1 to 10:

   • For $i = 1$: $1^3 - 2 = 1 - 2 = -1$
   • For $i = 2$: $2^3 - 2 = 8 - 2 = 6$
   • For $i = 3$: $3^3 - 2 = 27 - 2 = 25$
   • For $i = 4$: $4^3 - 2 = 64 - 2 = 62$
   • For $i = 5$: $5^3 - 2 = 125 - 2 = 123$
   • For $i = 6$: $6^3 - 2 = 216 - 2 = 214$
   • For $i = 7$: $7^3 - 2 = 343 - 2 = 341$
   • For $i = 8$: $8^3 - 2 = 512 - 2 = 510$
   • For $i = 9$: $9^3 - 2 = 729 - 2 = 727$
   • For $i = 10$: $10^3 - 2 = 1000 - 2 = 998$

2. Add the results:

$-1 + 6 + 25 + 62 + 123 + 214 + 341 + 510 + 727 + 998 = 3005$

Final Answer:

$\sum_{i=1}^{10} (i^3 - 2) = 3005$

Would you like further details on summation or any specific aspect of this calculation?

Here are 5 related questions you might find interesting:

1. How would the summation change if we evaluated $i^2 - 2$ instead of $i^3 - 2$?
2. What are some common techniques to simplify summations without calculating each term?
3. How does changing the bounds of summation (e.g., $i = 1$ to $i = 5$) affect the result?
4. What if we added a constant term inside the summation, like $\sum_{i=1}^{10} (i^3 + 3)$?
5. How can summations be applied to solve real-world problems?

Tip: Summation notation is a powerful tool in mathematics, especially useful for compactly expressing series and calculations involving sequences.