In Exercises 29–42, find each indicated sum. 9Σi=5 11

Question

Accepted Answer

Hello. Today we are asked to evaluate the indicated summation. So what we are given is the summation from I is equal 6-11 of 19. Now let's go ahead and figure out how many values of the index we're going to be evaluating for The starting value of the index can always be found at the bottom of the sigma notation and that's going to be equal to six. So we have I is equal to six as the starting value. Now let's figure out what the final value for the index is going to be. The final value of the index can be found at the top of the sigma symbol and that's going to be 11. So we're gonna want to evaluate from six following all the terms that come after going all the way to 11. Now, normally we would take these values and plug them in for any eye in the pattern. However, notice that our pattern is a constant and doesn't have any variables of I within it. That means that for every value of eye we're going to have the same value 19. So that means that we have is equal to six is equal to seven, I is equal to eight, I is equal to nine and I is equal to 10 and 11 And those are all going to produce the same value which is going to be 19. So what we have here is six instances of and that means that the total sum is going to be 19 plus itself six times. So We're going to add 19 with the South six times. Or in other words, we can go ahead and take 19 and multiply it by six. And doing this is going to give us the total sum of 114, which is going to be the answer to this summation. And with that being said, the solution to the problem is going to be C. So I hope this video helps you in understanding how to evaluate this type of summation, and I'll go ahead and see you all in the next video.

In Exercises 29–42, find each indicated sum. 9Σi=5 11

Key Concepts

Summation Notation

Constant Functions

Arithmetic Series

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