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. 5+7+9+11+⋯+ 31

Accepted Answer

Welcome back. I am so glad you're here. We are given a Some were given four plus nine plus plus 19. All the way up to plus 59 we are asked to rewrite this some using summation notation. We recall from previous lessons that summation notation has a sigma in the middle and above the sigma. We are given the upper limit of our summation. Below the sigma. We have our index. And here we're asked to use I for our index equal to our lower limit and to the right of our sigma is our formula. And we just need to identify those three parts. The upper limit, the formula and the lower limit. So first let's take a look at what's happening in our some. What's the difference between all of these numbers? Well, from 4-9, that's going up by five and from 9 to 14 that's also going up by five. So how would we represent that in a formula? Well we can say we have five times I. But the first number is excuse me, four. It doesn't start with five. So it's if the first value for i Is equal to one, then we're going to have five. I -1 for our formula. So we've identified the lower limit and the formula. But what's our upper limit? Well for this we take a look at our last term here in our some and we can set that equal to our formula, 59 equals five, I minus one. And now we can solve for I to find out the upper limit. So we can Add 1 to both sides And we'd have 60 equals five I. And then we can divide both sides by five, And we get I equals 12. We look at our answer choices and this matches with answer choice a well done, we'll catch you on the next one.

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. 5+7+9+11+⋯+ 31

Watch next