The expression shown in the image is the sum of binomial coefficients:

$\sum_{k=0}^{n} \binom{n}{k} = 2^n$

This is known as the binomial theorem and represents the expansion of the binomial expression $(1 + 1)^n$. It is derived from the fact that the sum of all the binomial coefficients for a given $n$ equals $2^n$.

The formula states that the sum of the binomial coefficients for any $n$ is equal to $2^n$, meaning the total number of subsets of a set with $n$ elements is $2^n$.

Would you like further explanation or details on how this result is derived?

Here are 5 related questions:

1. How do you expand $(1 + 1)^n$ using the binomial theorem?
2. What are binomial coefficients, and how are they calculated?
3. What is the significance of the result $2^n$ in combinatorics?
4. How does the binomial expansion relate to Pascal's triangle?
5. How can the binomial theorem be applied in probability theory?

Tip: To calculate the binomial coefficients $\binom{n}{k}$, you can use the formula $\binom{n}{k} = \frac{n!}{k!(n-k)!}$, where $n!$ represents the factorial of $n$.