Question: What is $\sum_{n=1}^5$?
1. **State the problem:** We want to find the value of the summation $$\sum_{n=1}^5 n$$ which means adding all integers from 1 to 5.
2. **Formula used:** The sum of the first $k$ natural numbers is given by the formula:
$$\sum_{n=1}^k n = \frac{k(k+1)}{2}$$
3. **Apply the formula:** Here, $k=5$, so:
$$\sum_{n=1}^5 n = \frac{5(5+1)}{2} = \frac{5 \times 6}{2}$$
4. **Simplify the expression:**
$$\frac{5 \times 6}{2} = \frac{\cancel{5} \times 6}{\cancel{2}} = 5 \times 3 = 15$$
5. **Final answer:**
$$\sum_{n=1}^5 n = 15$$
This means adding 1 + 2 + 3 + 4 + 5 equals 15.