In Exercises 55–60, express each sum using summation notation. Us...

Question

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+ar+ar2+⋯+ ar^12

Accepted Answer

Welcome back. I am so glad you're here. We are. Given this some A. R squared plus air to the fourth plus air to the sixth plus air to the eighth all the way up to a R. To the 30th. And were asked to rewrite this some using summation notation we recall from previous lessons that summation notation is going to have a sigma in the middle and then above the sigma is going to be the upper limit of the summation. What's below the sigma will be the index. And we're asked to use I as the index and that will be equal equal to the lower limit of the summation. And then to the right of the sigma is the formula. So we just have to evaluate for the upper limit. The lower limit and the formula of this sum. Alright there we can see our answer choices. Okay, so let's take a look at what's happening in our some what's happening as we go from a R squared to air to the fourth. Well, the degree of that are is changing. It's going from 2 to 4. How about from air to the fourth to air to the six? Well, again, the degree of that are is changing it's going up by two. So the A. And the R. Are remaining constant for our formula. And what's changing is the degree of the R. And we could take two times the index and that would give us our various degrees for our for the first the lower limit we look at a R squared and so we can set A. R squared equal to our formula and we ask ourselves what is I equal to hear? Well two times what equals two. That's one. So the lower limit Is equal to one. How about the upper limit? We look at the last term here a. r. to the 30th and set that equal to our formula A. R. to the two i. And what is I equal to hear? Well, two times what gives us 30. That's 15. So the upper limit is 15. We look at our answer choices and this is equal to answer choice. C. Well done. We'll catch you on the next one.

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In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+ar+ar2+⋯+ ar^12