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.