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The image contains a summation problem:

\[
\sum_{k=1}^{20} \left( 100k^2 - 500k + 100 \right)
\]

This means that we need to compute the sum of the expression \( 100k^2 - 500k + 100 \) as \( k \) runs from 1 to 20.

I will calculate this sum for you.

Let me compute that.The value of the summation 

\[
\sum_{k=1}^{20} \left( 100k^2 - 500k + 100 \right)
\]

is \( 184,000 \).

Would you like a detailed breakdown of how the summation was computed, or do you have any questions?

Here are some related questions you might find interesting:
1. What would happen if the summation upper limit changed to 50?
2. How would the result change if we added another term, like \( -200k^3 \)?
3. What is the general formula for summing quadratic expressions?
4. How does the growth rate of quadratic terms affect the sum?
5. Can we approximate this sum using integration for large upper limits?

**Tip:** Summation of polynomial expressions often grows faster with higher-degree terms, such as \( k^2 \).

Compute the summation from k=1 to 20 of the expression 100k^2 - 500k + 100.

This problem involves summing the quadratic expression 100k^2 - 500k + 100 from k=1 to 20. It covers algebraic concepts such as quadratic expressions, summation formulas for squares, and arithmetic series. Suitable for high school students in Grades 10-12.

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