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The problem reads:

**Express the given sum in summation notation.**

\[ 1 + 8 + 27 + 64 + 125 \]

**Choose the correct answer below:**

A. \( \sum_{k=1}^{5} k^3 \)  
B. \( \sum_{k=1}^{5} k^3 \)  
C. \( \sum_{k=1}^{5} k^4 \)  
D. \( \sum_{k=0}^{5} k^3 \)

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Would you like a detailed explanation on identifying the correct answer or help with understanding summation notation? 

### Further Related Questions
1. How do you identify patterns in sequences like \( 1, 8, 27, 64, 125 \)?
2. What is the difference between summing cubes and summing other powers?
3. How can we identify the starting index \( k = 1 \) versus \( k = 0 \)?
4. Why is \( k^3 \) an appropriate representation for this sequence?
5. How does changing the power of \( k \) (like \( k^4 \) in option C) affect the sum?

### Tip
Always check the first few terms in a sequence to see if they match common patterns (squares, cubes, etc.), which can guide you in choosing the right summation notation.

Express the given sum in summation notation.

1 + 8 + 27 + 64 + 125

Choose the correct answer below:
A. \( \sum_{k=1}^{5} k^3 \)
B. \( \sum_{k=1}^{5} k^3 \)
C. \( \sum_{k=1}^{5} k^4 \)
D. \( \sum_{k=0}^{5} k^3 \)

Learn how to express the sum of cubic numbers 1 + 8 + 27 + 64 + 125 in summation notation. Understand how to recognize patterns in sequences and choose the correct summation notation for this problem. Suitable for high school students in Grades 9-11.

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