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The image presents a question in Latvian asking, **"Which case correctly represents the expansion of the binomial (a + b)ⁿ using the summation notation?"** The answer options appear to represent versions of the **binomial theorem** formula.

### Correct formula for the **binomial theorem**:
\[
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
\]
Where:
- \( \binom{n}{k} \) is the binomial coefficient, often written as \( C^k_n \),
- \( a^{n-k} \) and \( b^k \) are the powers of \( a \) and \( b \), with the exponents summing to \( n \),
- The sum runs from \( k = 0 \) to \( k = n \).

### Evaluating the answer options:
The correct representation matches the first option:
\[
\sum_{k=0}^{n} C^k_n a^{n-k} b^k
\]
This is the proper binomial expansion.

Would you like more details about the binomial theorem or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How do you calculate binomial coefficients \( \binom{n}{k} \)?
2. What is the significance of the binomial theorem in combinatorics?
3. How can you apply the binomial theorem to expand powers of binomials like \( (x + y)^5 \)?
4. What are some real-world applications of the binomial expansion?
5. How does the binomial theorem relate to Pascal's Triangle?

**Tip:** The binomial theorem is particularly useful in probability theory and algebra for expanding expressions involving powers of sums.

Kurā gadījumā pareizi uzrakstīts Ņūtona binoma (a + b)^n izvirzījums ar summas pierakstu?

This problem explores the correct representation of Newton's binomial expansion for (a + b)^n using summation notation. The solution involves understanding the binomial theorem, a key concept in algebra and combinatorics, suitable for students in Grades 10-12.

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