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Chapter 8: Problem 34

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

Short Answer

Expert verified
The sum is 0.

Step by step solution

01

Substitute the lower bound

First, substitute the lowest value of \( k \) which is 1 into the function. \((1-3)(1+2) = -2 \)
02

Substitute the next value

Next, substitute the next value of \( k \), which is 2 into the function. \((2-3)(2+2) = -4 \)
03

Repeat the process

Continue substituting the remaining values of \( k \) into the function. \((3-3)(3+2) = 0 \) and \((4-3)(4+2) = 6 \)
04

Sum up the values

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

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