In Exercises 29–42, find each indicated sum. 5Σk=1 k(k+4)

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Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to evaluate the summation where we start at H is equal to one and we go to H is equal to seven and the expression is two H times X plus H plus three. So for the summation you can see that we're going to start with H is equal to one and we want to add up until H equals seven. So I'm going to go ahead and start figuring out what these terms are. So H one H is equal to one. My expression is two times one times one plus three. Fi simplify this, I have two times one plus three which is four. So when H is equal to one, I have eight. When H is equal to two the expression is two times multiplied by two plus three. If I simplify this I have four times five which is 20 H is equal to three. I have two times three, multiplied by 3-plus 3. If I simplify this two times three is 63 plus three is six and six times six is 36. When H is equal to four my expression is two times four, multiplied by four plus three. If I simplify this two times four is eight and four plus three is seven. So when H is equal to four I have eight times seven which is 56 and when H is equal to five my expression is two times five, multiplied by five plus three. If I simplify this two times five is 10, 5 plus three is eight. So when each is equal to five I get 80. When H is equal to six, my expression is two times 6 Time multiplied by 6-plus 3. If I simplify this two times six is 12 and six plus three is nine. So when H is equal to six I get 12 times nine which is 108. And finally the last term I need to solve is one. H is equal to seven. And recall that that is the highest term I need to solve because that is what is at the top of my summation. So when H is equal to seven, my expression is two times seven multiplied by seven plus three. So two times seven is 14 and seven plus three is 10. So when H is equal to seven I got 140. And from here you can see I solved all of the terms that I need to add together for this summation. So now I can go ahead and add those all together. So I have eight plus 20 plus 36 plus 56 plus +108 plus 1 40. So when I start adding these together, This summation is equal to 448. So this becomes my final answer for this summation. And you can see that that aligns with answer choice D. So hopefully this video helped and see you next time

In Exercises 29–42, find each indicated sum. 5Σk=1 k(k+4)

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