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Determine which of the following tests would be best to use to determine the convergence of the series below:9e 7Does the series converge or diverge?Select all that...

Question

Determine which of the following tests would be best to use to determine the convergence of the series below:9e 7Does the series converge or diverge?Select all that apply:Ratio TestRoot TestAlternating Series TestIntegral TestThe Series DivergesThe Series Converges

Determine which of the following tests would be best to use to determine the convergence of the series below: 9e 7 Does the series converge or diverge? Select all that apply: Ratio Test Root Test Alternating Series Test Integral Test The Series Diverges The Series Converges



Answers

Identify a convergence test for each of the following series. If necessary, explain how to simplify or rewrite the series before applying the convergence test. You do not need to carry out the convergence test. $$\sum_{k=3}^{\infty} \frac{1}{k \ln ^{7} k}$$

We'll even just on the farm minus seven. Okay. You fighting by K square? Giggles from going to infinity. Yeah, you. I'm going to use the ratio test now in the racial test, I need to compute the limit off the game. Risk one over. Okay, Can goes to infinity. And here we see that I gave this one. It must happen here first. Noticed that because of the absolute value. So we don't need to worry about minus, uh here anymore. And then would you get you go to the seventh Power cables one over the Cape Bliss one square, And then we divide by the A. K. So we need to multiplying by the reciprocal. So be the case going over seven. Okay, you noticed, Then we can consider seven. Okay, with this power here, and we can bring the by seven here outside the limit on. So these two here we can go them and should about you. Therefore, we get Echo. Just heaven times the limit on the game goes to infinity. They would have the gays Alma Gabor's one about you. Now we can push the limit inside the square here, and we get the seven Times Square on site, and some had a limit of the K over pay this one saying Just infinity honest that businessmen could you one. Therefore, we have the seven times one square and encourages seven. And because someone scripted and one therefore by the racial test, we conclude that this reason it will be no ive urgent.

Even. That's res under form for going about three per 70. Writing by nine K square minus one. Well, im ok and take us from going to infinity in this question. And we want to choose the test here and in the protests. And did you compute the limit? I'm the gay Britain. The absolutely a k k ghost infinity. Then we get a limit off the gave it off. The folk able to impress 70 leading by nine case grams minus one. They were having a Okay, Okay. Goes to infinity here. Noticed that we can cancel under K route with this better. OK, then we have left. Only the limit on the four came back to repressive and dividing by nine case Grandma minus one here. Not just that. The maximum power on the Thomas Barrett three dominate the maximum value in the bottom onion. About you. Therefore, this limit where you go to the infinity now and the infinite is bigger than one. Therefore, by the test mysteries, it would be divergent

Even under fall. Okay. Route under Gaiman's one doesn't about two. Okay. Takers from going to infinite day in this question and 20 years down with destiny. And in the retest and inter compute the limit off the rhythm the absolute I Okay, carrying goes to infinity and then the nation Glenda gave it off. Okay, route off the K minus one talking about the UK Kangas to infinity. They noticed that we can concerned the Beirut with just about getting here and then we have left, but only, uh lim Ah ah gave root off a minus one. How would you say another stem? Skg infinity This one will go to one and then we have the minus one. That was too. And then we get equal to the so squarely coaches 00 small it and one therefore by the task we conclude that this is how it will be convergent

Even suits under four months. One about okay and then gave birth. Three of on, uh, squared on cable eight plus one here. Notice that we have the isn't it? Yeah, because I was That's fund. Absolutely convergent first and for the absolutely regions. And it's considered this result of form gay poetry. I was square with under caper and press one and take it from one to infinity. Here, I need to come and use the limit Racial test here and interest and limiters that that I would compare with that serves enough form. Came about three over square. Okay, well, I eat and then doesn't come recently find and we send one over k Goes from one to infinity Were not listening. Is the innocents harmonic series that fired? It will be divergent. Then we compute the limit off one of a k Over came three over square on the cable And this one we're seeing this limit EKO tuna square rhythm agree about anything plus one over We can register Runas Exe credit on the cable and and we say we can consider this to hand and we will have a limit off one Bless one of a tape about eight and now we can escape goes to infinity. This this one goes to the zero forgetting coaches with 1 to 11 has created an zero therefore by the limit ratio test and this divergent and this one here we conclude that this trees here will be divergent and that we need to test for the conditionally convergent and one way to do it. Computer limit off the cable three over Scrabble The game for our eight plus one Going to infinity here Noticed that the maximum amount on the Tommies about three the maximum about in the bottom after we assume to find a square root with about eight here it would be could go far. So cable forward dominated. The came about three for this limit coaches zero and then we conclude that this reason be convergent and as a result, final conclusion will be This is not absolutely convergent, but it is conditionally convergent


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