We are asked to evaluate the sum $\sum_{n=4}^{6} (n-1)$. This means we need to find the sum of the expression $n-1$ as $n$ takes on the values 4, 5, and 6.

1. Problem Description

We are asked to evaluate the sum $\sum_{n=4}^{6} (n-1)$. This means we need to find the sum of the expression $n-1$ as $n$ takes on the values 4, 5, and

6.

2. Solution Steps

We will substitute each value of $n$ into the expression $n-1$ and then add the results.

For $n=4$, the expression $n-1$ evaluates to $4-1=3$.

For $n=5$, the expression $n-1$ evaluates to $5-1=4$.

For $n=6$, the expression $n-1$ evaluates to $6-1=5$.

The sum is therefore $3+4+5$.

$3 + 4 + 5 = 7 + 5 = 12$.

3. Final Answer

12