What if the problem asked for \( \sum_{k=3}^{5}(k-2)(k-3) \)

To solve the problem \( \sum_{k=3}^{5}(k-2)(k-3) \), first, we can evaluate the expression for each value of \( k \) from 3 to 5. For \( k=3 \), \( (k-2)(k-3) \) becomes \( (3-2)(3-3) = 1 \cdot 0 = 0 \). For \( k=4 \), it becomes \( (4-2)(4-3) = 2 \cdot 1 = 2 \). Lastly, for \( k=5 \), it is \( (5-2)(5-3) = 3 \cdot 2 = 6 \). Now sum these results: \( 0 + 2 + 6 = 8 \). Another note is that the expression \( (k-2)(k-3) \) can be represented as \( k^2 - 5k + 6 \). So, if you encountered a larger sum, it might be easier to sum the individual terms in the polynomial expression instead – sometimes breaking it down can help prevent errors in more complex calculations.