Problem 34 - College Algebra

Question

Find each indicated sum. $$\sum_{k=1}^{4}(k-3)(k+2)$$

Step-by-Step Solution

Answer

The sum is 0.

Step 1: Substitute the lower bound

First, substitute the lowest value of \( k \) which is 1 into the function. \((1-3)(1+2) = -2 \)

Step 2: Substitute the next value

Next, substitute the next value of \( k \), which is 2 into the function. \((2-3)(2+2) = -4 \)

Step 3: Repeat the process

Continue substituting the remaining values of \( k \) into the function. \((3-3)(3+2) = 0 \) and \((4-3)(4+2) = 6 \)

Step 4: Sum up the values

Finally, calculate the sum of the results obtained from each substitution into the function. \(-2 -4 + 0 + 6 = 0 \)