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Deter mine Whether the Seguence is Convergent ^Q if 4+is qveraet: Convergeat1 fina limit an (1-3)"(2...

Question

Deter mine Whether the Seguence is Convergent ^Q if 4+is qveraet: Convergeat1 fina limit an (1-3)"(2

Deter mine Whether the Seguence is Convergent ^Q if 4+is qveraet: Convergeat1 fina limit an (1-3)" (2



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In Exercises 11–20, determine whether the sequence converges or diverges. If it converges, give the limit.
$$\{3 n-1\}$$

For this sequence here. Three and miles one over two months. Three. And it's required to find out of this sequence. School verges old. I would, in other words, when N is infinity goes to infinity. The value of this sequence would be a certain number, which means if it converges or not, if not this. When N is goingto infinity, it gives and finish your minds and pretty or sometimes it's not the number. Then afterwards, another number. Then it diverges, which means that the element that doesn't exist so here, when to find out how. If this converted diverges, then we have to set the limits one day element off this when N is goingto in plenty now when there is going to infinity since here in and it's got a 20 one of the rose off. Finding the limit is to look at the the highest power or highest degree on the numerator on the highest degree into doing it. So the highest degree here, and three and and the highest degree off the donator is minus the three end. So now ignoring it's a ignoring the mice one and two would be limits and is going to infinity three and or were Linus three? These are the highest power or highest degree and innovator and ignorant. So plea and over my three ends and with any would be counseled and three of our minds three would be minus one. So the limit here is minus one, then says dim, it is minus one means that the sequence converges two minus one when n is goingto infinity. So whatever the answer, the end or the term would be equals two minus one, so it converges to minus one.

And this a question. It's given the the 1st 4 terms in the seaQuest, and you have to find out if this seek waas, converge or diverge. In other words, if the stick was diverge, which means that it would go for infinity but infinite number of sequences it would go for and fancy numbers. So just go either toe plus infinity or minus infinity on If it's converges, then it will go toe a really certain number whatever and is 100 in is 1000 and it just go with Goto. I really specific certain number. So the first time is warmed them forward and lie in the 16th which is given as the end of term with the end squared. So, in order to find out whether this would govern or diversion, then we have to use the limit. We're en go to infinity, so limit off this little which is n squared on end is goingto on Francie, if we substitute just infinity here in this limit, it gives and for the squad which is infinite, so didn't the sick ones would go to infinity number, but the value of big will go to infinity when n is going to infinity. So means it means that this is divert. So the sequence it diverges on there's no specific a number that this it's sequence would go to it will read toe more than 5000 more than 50,000. It was ridge toe and 50 and influencing number as the end. It's squared and for antique was 52 b 50 square foot and it was were herded with the model square and this would go for infinity. So I hope you got this on the answer would be divers.

You have a new series. It iss a n is equal to and raised to the third power minus one. Everything over Andi, I think I'm going to do this. Everything for and raised to the third Power. Okay, so that is our series. Um, if this year is working virgin, then we should be able to find, um if it increases or decreases. If it increases, then it should, um, have a boundary above. She rebounded above an increasing. That means that it converges or if it's found a bolo on decreases. So conversions increasing us, hounded above or decreasing, founded Well, so for that, we're gonna play in some number and see what's happening here. A one is equal to one minus one over one. Right. So, Cyril, over too, Which is Let's go with the 2nd 1 A two 22 lines to to 1/3 which is each minus one divided by a plus one, which is seven over nine. Oh, let's go with a 10 huh? I intend to Her powers 1000 moons. One over 1000 plus one just equal to 999 over 1001. Just 0.98 so well, the Siri's eventually reach, for example, too. Can't It? Seems like it has a cap on one so we can go ahead and take a limit. Women ISS and goes to infinity. What do we get for the top part? Since they both have an Henry Sue third power, we only need to look at the coefficients in front of the ends. So we have one and they still have power over one, and ratios are power, so the limit is going to be just one over one, which is one. So we were right. It does have a boundary above by one, and it seems to be increasing. So it is increasing, has a boundary, so it does converge, and it converges to

Hello and welcome. We are looking at Chapter two, Section one problem night. We were asked to take a look at this sequence and determine whether or not it converges. And if it converges final in it. So, uh, I recommend is jumping right into the limit with a question like this. Um, we have won over three and before. Now, if we think about this as becomes a little more clear, if we think about this is 1/3 times one over end of the fourth, um, just lets us break the limit up a little bit more clearly. So by the limit laws, we can write this as 1/3 times the limit as and goes to infinity of one over end of the fourth. So this step right here isn't necessary. You could jump jump straight from here to here if you wanted, but I just want to make it extra clear what we were doing. So that's just by the limit loss. There's a nice box in your textbook. You can look at those. Um so this right here there's another box in your tactics book that talks about things that look like this. So it says the limit as and goes to infinity of one over N to the P is zero on one condition. He has to be greater than zero. So the exponents that end is being raised to has to be greater than zero. So four Our case here is definitely greater than zero. So we can use this property here and show that this equals. I'm continuing my work kind of down here 1/3. And if we take that limit, times zero Another way you can think about is as n gets large. The denominator gets very large, too. And a large denominator makes for a small number. Won over a 1,000,000 is a lot different than 1/2 won over million's a lot smaller, So large denominator, equal, small number. If you take that denominator to infinity, the number of becomes zero. That's another way to think about. Regardless you get here. So this converges and it converges to zero. Now it would diverge if we got infinity as our as the result of our limit. But since it goes to zero, since it goes to a number, that's not infinity. We're good


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