/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 Find each indicated sum. $$\su... [FREE SOLUTION] | 91影视

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Chapter 14: Problem 22

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

Short Answer

Expert verified
-4

Step by step solution

01

Expand the Expression

First, expand the expression within the summation, \((k-3)(k+2)\), which gives \(k^2 - k - 6\). So, the exercise now becomes \(\sum_{k=1}^{4} (k^2 - k - 6)\).
02

Implement the Summation

Now, replace \(k\) in the expression \(k^2 - k - 6\) with the values from 1 to 4, one at a time, and add up the results. This gives \((1^2 - 1 - 6) + (2^2 - 2 - 6) + (3^2 - 3 - 6) + (4^2 - 4 - 6)\) which simplifies to \(-6 + -4 + 0 + 6\).
03

Calculate the Final Sum

Finally sum up the values obtained in the previous step to get \(-4\).

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Most popular questions from this chapter

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