In Exercises 43–54, express each sum using summation notation. Us...

Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

Accepted Answer

Hello today we're going to be representing the following some using summation notation. And we're going to represent the index and lower limit of the summation as K. And five. So the lower limit for our summation is going to be five or in other words is going to be K is equal to five. And that means that we're going to be starting the some with five and plugging in every number for all the following terms. All the way until the final value, which is going to be the index. So we're gonna be plugging in K is equal to 56 and seven all the way to our final value. Now let's take a look at the first term of the sum. The first term is five. The second term is six And the third term is seven. Notice how the first three terms accurately represent the first three values of the index of the summation. That means that we're just taking the values of the index and plugging it in directly into our summation. And that means that the pattern to the sum, it's just going to be came because if K is equal to five then the first term is going to be five. If K is equal to six, the first term is going to be six and if K is equal to seven, the third term is going to be seven. With that being said, we need to find the index of the summation now and the index is just the final value here. The final term of the sum is 35. And if we just plug in 35 into our pattern, we get 35. So that means that the final, the final value of the index is going to be 35. Or in other words our upper limit Is going to be K is equal to 35. Now let's go ahead and write this in the form of a summation notation. We first start by writing the symbol sigma and we put the lower limit or starting value at the bottom, which is going to be K is equal to five. Our final value for K is going to go to the top of sigma which in this case is 35. And we put the pattern for the sum, which in this case is K. And this is going to be the summation notation for the given some. And that means that the answer to this problem is going to be. Be so. I hope this video helps you in understanding how to find the summation notation. And I'll go ahead and see you all in the next video

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

Key Concepts

Summation Notation

Index of Summation

Arithmetic Series

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