5

Use the nth-term test for divergence t0 show that the series divergent or state that the test /S inconclusive.2 n+2 n=oSelect the correct choice below and necessary...

Question

Use the nth-term test for divergence t0 show that the series divergent or state that the test /S inconclusive.2 n+2 n=oSelect the correct choice below and necessary; fill in (he answer box wilhin your choice.0 A: The test IS inconclusive because0 B The selos diverges because + 20 and Iails Io existIne sorios diverges bocauso M 'OOand Iails Io oxisiThe series diverges because |im M-'0exists and IS equal to

Use the nth-term test for divergence t0 show that the series divergent or state that the test /S inconclusive. 2 n+2 n=o Select the correct choice below and necessary; fill in (he answer box wilhin your choice. 0 A: The test IS inconclusive because 0 B The selos diverges because + 2 0 and Iails Io exist Ine sorios diverges bocauso M 'OO and Iails Io oxisi The series diverges because |im M-'0 exists and IS equal to



Answers

Use the $n$ th-Term Test for divergence to show that the series is divergent, or state that the test is inconclusive. $$\sum_{n=0}^{\infty} \frac{e^{n}}{e^{n}+n}$$

You were given following Siri's and you're asked to use a term test to determine just seriousness time. Urgent. First thing that you do is you take the limit. It was an your purchase, infinity facia, and which in this case, is on over one over which is equal to the limit. This other approaches infinity. Both I think it out. You can shock throughout the negatives those one that is needed limit as any purchase and plenty of how earned, which is just simply equal to negative infinity. So you know that was the limit. Has a new approaches infinity from eight to end. This is equal to zero. Then if this is not true than this, Siri's is divergent. So you just found that the limit of Ellen of a one over and is night of Vivendi and this is not equal to zero. So you know that the Siri's diverges based off the end test test for divert, gets

Hello, everybody. This is Kevin Truck with new Murad. Let's look at what this infinite Siri's might add up to. Well, there's a lot that's going on for this, but we do know that we're gonna be starting off with is is putting in a value of one and then indexing it every single term from there. So we've got one times one plus one. It's to over one plus two is three plus one times one plus three would be four. We're going to get something along. These lines will be adding that to the next index well behind right that we have two times three and then each of this is going to go up by one is also four times five, and we're gonna continue to add that through over and over and over again. Now, notice that we do have what looks like a denominator that is gonna be larger than the numerator. But instead of trying Teoh solve all this out, we can do what's called an end value on term test to find out whether or not this is going to decrease fast enough that I don't accidentally blow up to infinity. And so here's kind of what that looks like. Let's consider if at the end of all of this, at the end of all of this, I am going to be still adding terms that are not zero village, which there is no end. So really, what? We're talking about its limits here. So let's structure and thought little bit more properly. Let's look at what is the limit as n goes to infinity of end times and plus one over and plus two times and plus three. And really, what we're checking by doing this is we're saying, If I continue doing this forever, never, never, never will I still be adding things. Or will I theoretically eventually be adding zero at my forever term? So let's go ahead and work this on out. What? We can recognize that if I was just to kind of plug this and I'm gonna write this in brackets, because this is this is me being sloppy, but it's a nice little note to give yourself. I plugged in infinity here, which you can't do. It's not a number, but if we're going Teoh allow ourselves a little bit of error, we would see that we're gonna have infinity over infinity again. Not proper mathematics here, but we can recognize that we do have it's called indeterminate form. And so we might use what's called Loba tells rule to simplify out this This problem so low Beatles Rule says that if I have something which would have evaluated out to infinity over infinity, if I was incredibly sloppy, that I can simply do the derivative of the numerator and then the denominator. And that will be a much easier, much easier ratio to consider as I do the limits. Okay, so we're gonna do a product rule in top because we do see that we have end times n plus one. It's gonna be derivative of the first times. The second as is so it's gonna be endless one plus the first, as is times the driver of the second, which is gonna be one over. And then the bottom is going to the same thing driven or the first is gonna just simply be one times the second, as is, plus the derivative of the first times. The second as is now, I did forget some notation here. Remember that this Onley true love hotels rule on Lee works If you are still talking about limits, you're not allowed to step out of limit thought here. So all this is going to simplify out to sea Teoh. Let's see n plus one plus ends, too, and plus one over and then we have en plus two plus n plus three. So to end, plus five now we could actually do Loki tells Rule one more time. Gonna be a little bit simpler this time. Notice that there is a way to evaluate this by simply dividing by the largest and term over here. But I'll leave that as a as a exercise for another video. Lovato's real one, more time driven with the numerator is going to simply be too driven other than denominator is simply going to be, too. We're gonna include the fact that we're talking about the limits here, but the limit as N goes to infinity of 2/2 is just gonna be the limit as N goes to infinity of a constant. So it's just going to simply be that constant. So this is going to be ah, value of one, and what we can say is that because if we re contextualized all the math that we've done, the forever term, if you will, the forever term that I am adding into this series is one. So I'm adding a forever number off ones or things that are not zero is a very loose way of interpreting it. But essentially, what we can conclude is that because this serious does not decrease down to zero ever that I am going Teoh diverge. And this entire Syria's is going Teoh blow up to infinity. So we can kind of just put a little notation here and say that this thing, if I was gonna continue it forever, would approach infinity and grow in value. Okay, it's going Teoh diverge. So you could say maybe something like diverge to or towards infinity.

All right, everybody, welcome. This is Kevin Truck with New Murad. Here we have an infinite Siris of what looks like end over end squared plus three. Now there's a means of evaluating whether or not this is going to converge or diverge. Called the term test. Essentially, what it's asking is it was going to do this salvation forever. Would I eventually be adding nothing mawr to my total or what I'd be adding something indefinitely more to my total. And really, what we're gonna test is what is it that I'm adding as I approach my forever term, if you will grant me a little bit of loose speak right there. No, there's, ah way to test this where we just simply consider that forever term. So we're really looking at the limit is an approaches infinity of this expression and over and squared plus three now lumpy tiles rule. If you're familiar with it, would provide a nice way of evaluating this because I do get an indeterminant form. But I'm also gonna in this video, I'm going to look at just simply comparing the magnitudes of each of these terms. Somebody is a little bit a technique where we just simply divide through by the largest value so noticed that it is fair in limits to divide by, ah, cards to divide by variables. Normally, I wouldn't be allowed to do this in algebra because that variable could be a zero. But limits don't care about moments of dis continuity. They care about overall structures. So essentially what I can say is I can divide the top by Let's propose M squared and I will divide everything of the bottom by in squared two. So let's do end squared over and squared, plus three over X squared. This would be then the limit as n goes to infinity of one over end over one plus three over and scored. So essentially all we've done is we've just taken away the magnitude of the largest term, and we're considering how everything else is changing in relation to that. What we do know that one over n is n goes to infinity is gonna be a zero and that one plus three over and square. It is gonna be one plus zero as any goes to inferior. So I've got 1/1 plus zero, and so this says that I do have AH value of zero. So I am going to eventually be adding It looks like numbers that are of the zeroth power or zeroth size. But that doesn't tell me that I'm going to get there fast enough so I can kind of write a little note to myself here. That says, the term test, the inter term test for divergence. And that's the important part. This test four divergence is inconclusive, and it's inconclusive because I was able Teoh, too. I wasn't able to confirm that. I did always add values that were larger than one. But it doesn't necessarily say anything about how this structure as a whole if it goes down to adding values of zero mega.

You were given a fallen Siri's and you're asked this term in using unturned test for divergent. If this series is divergent so you just find a low. It was approaches infinity of co sign of one over which is equal to want. So you know, that limit was an approaches Infinity data on it was his hero. If this is not true, then this series is divergent. So you just found that the limit is one So you know this is not true. Therefore you know the Siri's diverges


Similar Solved Questions

5 answers
Find Whal pZaces Find the Find the the Mhere first the probability xf quantile Iv per tha ants 1 andomly randomly nndomly forest seiecthu electad [ Fn voetealedd 3 the acre distributed between 1 the 795 forest 1 Rouind numder 3 42,068 pue 1 standard h
Find Whal pZaces Find the Find the the Mhere first the probability xf quantile Iv per tha ants 1 andomly randomly nndomly forest seiecthu electad [ Fn voetealedd 3 the acre distributed between 1 the 795 forest 1 Rouind numder 3 42,068 pue 1 standard h...
3 answers
What proportion of shoppers at a large appliance store make big-ticket purchase? To estimate the proportions within 10% and be 95% confident of the results; how large a sample should be taken?Tost StatisticFormula #:Distribution:Confidence LovolLeft Critical Value:Right Critical Value:Sample size
What proportion of shoppers at a large appliance store make big-ticket purchase? To estimate the proportions within 10% and be 95% confident of the results; how large a sample should be taken? Tost Statistic Formula #: Distribution: Confidence Lovol Left Critical Value: Right Critical Value: Sample ...
5 answers
4. The monthly electric bills in a point city are normally distributed with a mean of $135 and a standard deviation of $22. Find the X-value corresponding to a Z-score of 1.65.Your answer5. Find z if P(Z < 2) = 0.062pointYour answer
4. The monthly electric bills in a point city are normally distributed with a mean of $135 and a standard deviation of $22. Find the X-value corresponding to a Z-score of 1.65. Your answer 5. Find z if P(Z < 2) = 0.062 point Your answer...
5 answers
LetAand define T R2_R? by T(x) = Ax. Find the images under T of u =andv=Shor wolk.cllck (0 salect your answer(s).
LetA and define T R2_R? by T(x) = Ax. Find the images under T of u = andv= Shor wolk. cllck (0 salect your answer(s)....
5 answers
6. Given the data in the table below, AHPrxn for the reaction Ca(OH)z (2H,AsO4 Ca(HzAsO4)2 2Hz0kJSubstanc AH'€ (kJlmol) Ca(OH)2 986.6 H3AsO4 ~900.4 Ca(HzAsO4)2 -2346.0 H20 2k -285.9A)-744.9 B) -4519 -4219 -130.4 E) -76.4
6. Given the data in the table below, AHPrxn for the reaction Ca(OH)z (2H,AsO4 Ca(HzAsO4)2 2Hz0 kJ Substanc AH'€ (kJlmol) Ca(OH)2 986.6 H3AsO4 ~900.4 Ca(HzAsO4)2 -2346.0 H20 2k -285.9 A)-744.9 B) -4519 -4219 -130.4 E) -76.4...
5 answers
A € Zu Find a number such as41 000 000 000 000 00 4 10128 456 789 =a (mod 41) .
a € Zu Find a number such as 41 000 000 000 000 00 4 10128 456 789 =a (mod 41) ....
5 answers
Problem 3(4 points)Express the function f(z) In(1 T) as a power seriesWhat is R, the radius of convergence, for this power series? R
Problem 3 (4 points) Express the function f(z) In(1 T) as a power series What is R, the radius of convergence, for this power series? R...
5 answers
Flag questionLet X ={a,b,C,d,e} and let s/ = {(a,b} {a,0},{d}} The number of elements of the topology T having as a subbase is1211135101415Previous pageNext page
Flag question Let X ={a,b,C,d,e} and let s/ = {(a,b} {a,0},{d}} The number of elements of the topology T having as a subbase is 12 11 13 5 10 14 15 Previous page Next page...
5 answers
Ify= csc(x) Ithen y' Select one Or more:1+cos?(x) sin?(x)CSC?6) - csc(x)2csc? (x) - csc(x)sin?(x)+2cos2(x) sin? (x)csc(x)t ZcscixlcoP(x)
Ify= csc(x) Ithen y' Select one Or more: 1+cos?(x) sin?(x) CSC ?6) - csc(x) 2csc? (x) - csc(x) sin?(x)+2cos2(x) sin? (x) csc(x)t ZcscixlcoP(x)...
1 answers
Find the area of the indicated surface. Make a sketch in each case. The part of the sphere $x^{2}+y^{2}+z^{2}=a^{2}$ inside the elliptic cylinder $b^{2} x^{2}+a^{2} y^{2}=a^{2} b^{2}$, where $0<b \leq a$.
Find the area of the indicated surface. Make a sketch in each case. The part of the sphere $x^{2}+y^{2}+z^{2}=a^{2}$ inside the elliptic cylinder $b^{2} x^{2}+a^{2} y^{2}=a^{2} b^{2}$, where $0<b \leq a$....
5 answers
How many differentiable functions f : 2 R are there such that f(z)' IQ(z)f(z)? zQ()f(z)? rf(z) 0, where Q(z) the unique quadratic polynomial satisfying Q(z? +1) = Q(z)? + Q(z) +
How many differentiable functions f : 2 R are there such that f(z)' IQ(z)f(z)? zQ()f(z)? rf(z) 0, where Q(z) the unique quadratic polynomial satisfying Q(z? +1) = Q(z)? + Q(z) +...
5 answers
6,664 cm? d mateial aaabia @ Malu 4ta1 mn # 5lie basecoraudd Indt# uaest possble volma 0 tabxNot: Wrna ony 42 nunanz4(uilo 0' {no voumo Ia unitz aro Jvondy #Tron Ktto {n0 fMI (ador noln* Deciige dodroumaoon 005i Fanati poasiblo votro Ihe bDu
6,664 cm? d mateial aaabia @ Malu 4ta1 mn # 5lie base coraudd Indt# uaest possble volma 0 tabx Not: Wrna ony 42 nunanz4(uilo 0' {no voumo Ia unitz aro Jvondy #Tron Ktto {n0 fMI (ador noln* Deciige dodroumaoon 005i Fanati poasiblo votro Ihe bDu...
5 answers
Identify the terms of the expression.$-7 x+4 x$
Identify the terms of the expression. $-7 x+4 x$...
5 answers
8f (9(1,1),h(1,1)) = Ox8f (9(1,1),h(1,1)) = dyNow use the chain rule to compute the partial derivatives of the composite function at the point (1,1):22 (1,1) Du82 (1,1) dv
8f (9(1,1),h(1,1)) = Ox 8f (9(1,1),h(1,1)) = dy Now use the chain rule to compute the partial derivatives of the composite function at the point (1,1): 22 (1,1) Du 82 (1,1) dv...
5 answers
PPM100137 1391593 95151 152 153 154306090 Mass Me120150180OhOHOHOHOHOH
PPM 100 137 139 15 93 95 151 152 153 154 30 60 90 Mass Me 120 150 180 Oh OH OH OH OH OH...
5 answers
Find EQ for the following galvanic cells Show your work Mg(s) | Mg?-(aq) IlPb?-(aq) Pb(s)Cr t(aq) | Cr(s) Ag(s) | Agt(aq)(6) Consider galvanic cell. Do electrons flow from anode t0 cathode, or from cathode to anode? Explain how you know.Within the salt bridge, do anions flow towards the anode or the cathode? Explain how you know.
Find EQ for the following galvanic cells Show your work Mg(s) | Mg?-(aq) IlPb?-(aq) Pb(s) Cr t(aq) | Cr(s) Ag(s) | Agt(aq) (6) Consider galvanic cell. Do electrons flow from anode t0 cathode, or from cathode to anode? Explain how you know. Within the salt bridge, do anions flow towards the anode or ...

-- 0.026267--