5

Uze Hadaurin series in the table below to obtaln the Madaurin series for the glven functlon_ {x) = 6e*Co , = E(-IV" (u)R=Lln `X(-[J"R=KLAU~u-4+#"=2R=...

Question

Uze Hadaurin series in the table below to obtaln the Madaurin series for the glven functlon_ {x) = 6e*Co , = E(-IV" (u)R=Lln `X(-[J"R=KLAU~u-4+#"=2R=]

Uze Hadaurin series in the table below to obtaln the Madaurin series for the glven functlon_ {x) = 6e* Co , = E(-IV" (u) R= Lln ` X(-[J" R= KL AU~u-4 +#" =2 R=]



Answers

Use a graphing calculator to evaluate each series. $S$ $$\sum_{r=3}^{10}\left(k^{2}-4 k+7\right)$$

This question gives us some information. It tells me that some of the first end is 315 when our is 0.5 and and it's six, and it wants us to find a two. Okay, so we're gonna use this information these three pieces to find a one by saying this is my formula S N is equal to a one under one minus art of the end divided by one minus R. So that means that 315 is then a one onto one minus 0.5 to the sixth power divided by one minus 0.5. Excuse me. So then 315 is equal to a one multiplied by whatever. One minus 10.5 of the six power is that on our calculator. And I'm not showing you my tell a few later on the screen, but you should fall along to make sure that you're getting the same numbers. So, um, I'm getting 0.984375 and then I'm dividing that by 0.5. So that means that a one is gonna be 315 times 0.5, bringing this up by multiplying and then divided by this 0.984375 So we get anyone to be again on our leader, um, 160 and then we can find a, too. So I could say, therefore, a two is just a one. Times are so it's 160 times 1600.5, and so it comes out to a T, and that's my final answer.

We have a # 64. Okay, this is K equal to two 2 6, 5-. Okay now we have to first write out the terms. So let us start with equal to two, 5 -2 into two plus five -2 and 2 3 bless 5 -2-4 less 5 -25. Place 5 -2 into six. So this is 5 -4, one plus 5 -6 -1. Bless 5 -8 -3 plus five minus 10 minus five plus five minus 12 minus seven. So this will be -15. Thank you.

Here we are given a finite arithmetic sequence. 17.3 19.6 21.9 24.2 and 26.5, and asked to write the series that goes with it, which would be adding up all of the terms of the sequence, 17.3 plus 19.6 plus 21.9 plus 24.2 plus 26.5. Once we have written are complete Siri's, we are now asked to evaluate and we can do that by adding up each of the five terms one by one or all at once. Just be sure to line up the decimal point if you choose to do it by hand or if you would prefer you can use the formula. Capital s sub n is equal to and over too multiplied by the sum of a sub one plus a sub n the capital s sub and is referring to the total sum of our series. Ah, and representing the number of terms which in this case is going to be five and then also further into our formula. You can see we have a sub one, which is referring to the first term in our sequence and a sub n which is, and being five in this case is gonna be the fifth or final term in the sequence. So when we go to plug everything in, we have five divided by two ace of one. Our first term is 17.3 plus ace of an or a sub five, our last term, which is 26.5. And from here we would evaluate using our order of operations, which indicates we need to take care of large groupings first. So 17.3 plus 26.5. Please be shorter. Line up the decimals. So we will end up with three plus five would give us he ate right to the right of the decimal point. We add up the one's position, the six in the seven. We end up with 13. So all right, down the three carry the one. So we have one plus two plus one, which is for so are some of 17.3 plus 26.5 is 43.8, multiplied by five and divided by two would give us our final sum of 100 nine point five. As a recap, we were asked to write the series of the sequence, which is written in Blue, and as to evaluate the final sum, which is 109.5.

Given this. He's under form from one to infinity. Through times for time. Absolute. You and they Invited by Jul Times five times after duck tree and minus one. And certainly Bowers too. And now we have expelled. And do you find the radius of the convergence? We need to do the limit ratio test where we need to computer limit. Oh, I am just one. Do you fighting? But I am. And we get food. I end this one. We're gonna go to comes for up to the U. N. And then after we beat that, you and us too. And now let me rent clear here to end this too. I know Dividing by the Jew times five after the three a minus one. And now the next time will be the three and, um, less too. And that everything would be about you times the x Bella And here and now way the fighting. But I am so we want to live by the reciprocal. So which again, huh? Geo items Five after the three am Manasquan dividing by June terms far up, Judah to and about you. And now we would divide by the expel and isn't be endless one here. Sorry about that. And now you explain. And against it would dispel on the X on the top here and now we will have all of the term here. Cancer. I went on longer term here. I'm just one against it. I went on this one for the X is a constant so I can bring in outside their farts again. The absolute of thanks. Inside we have a limit and goes to infinity. And now since I will have, uh, to endless too they riding by and, uh, three endless to about you So we should get equal. Absolute Thanks. This limit we can put inside the square. Therefore, we have the square outside and so have a limit. Angus to infinity. To enlist. To amber tree and rest to and as Angus to infinity. This name it goes to do at victory here. So we have the Jew and victory about you. Then we get in. Could you for absolute X smaller than I wanted to have a convergent Just limit must be smaller than one. Yeah, Far doesn't advice down. The absolutely will be smaller than out of far. And they found this one last tender Raiders under convergence. We should deny out of far and initially answer


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