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Please help me with yet ANOTHER infinite series question 
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#1
Feb1512, 01:54 PM

P: 116

1. The problem statement, all variables and given/known data
Ugh really getting frustrated at not being able to keep up with math.. Find the set of x for which the series converges AND find the sum of the series at these values. s=[itex]\sum^{k=infinity}_{k=0}[/itex] [itex]\frac{(x+7)^{k}}{3^{k}}[/itex] 2. Relevant equations 3. The attempt at a solution OK, by using the ratio test I find the set to be x=(10,4). I entered this in, and this is correct. But I am very confused about the second part of the question.. starting with the wording. Is it asking me to find the sum at x=10, THEN the sum at x=4, and then add them? I ask this because there is only ONE field in which to input the answer. But regardless of whether it is asking that, I am finding it difficult to find the sum when x=10. I get the sum of (1)[itex]^{k}[/itex] from k=0 to k=n as n approaches infinity. So I get the sum of s=11+11+1+...(1)[itex]^{n1}[/itex]+(1)[itex]^{n}[/itex] My initial thought was that s=0, because all the terms would cancel out. Then I realized, it could also equal 1 because as n approaches infinity, the terms would always change between 1 and 1. So I couldn't decide between the two. But THEN I entered it into wolfram alpha, and it says that the series is equal to 1/2! How does this even make sense? Can someone explain please? But I am very confused AGAIN for the following: When I try x=4, I get the sum of 1+1+1+1+1+... n times (so it should be infinity). And if the original question is asking to add these series together, then it shouldn't matter whether the sum when x=10 is 0, 1, or even 1/2, because any of those values plus infinity is equal to infinity. But when I input this into the answer area, I get it wrong. What am I doing wrong? Thanks. 


#2
Feb1512, 02:16 PM

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Surely you have seen such sums hundreds of times already. To me the question seems perfectly clear: evaluate S(x) for any value of x in the convergence region. It does not ask you to sum S(x) for different values of x, because that would make no sense at all: summing S(x) for a continuous x is not a defined operation (although integrating S(x) would be). Certainly you should never attempt to add the values of S at the endpoints of the convergence region because these values may not exist: convergence regions of infinite series are open intervals, and the series might (usually does) diverge at the endpoints of these regions. PS: in tex the command for ∞ is "\infty", not "\infinity" or "infinity". RGV 


#3
Feb1512, 03:14 PM

P: 116

Thanks anyways 


#4
Feb1512, 03:51 PM

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Please help me with yet ANOTHER infinite series question



#5
Feb1512, 04:35 PM

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Why would you suppose I was imptatient or annoyed?YOU used Tex, but got the infinity sign wrong, so I thought you might like information on how to do it right. As for never having seen such a series before: if you haven't, I am truly surprised, especially in a "Calculus and beyond" forum.
RGV 


#6
Feb1512, 04:49 PM

P: 116

Also, I went to a terrible high school. Almost none of my graduating class went on to postsecondary education. I'm almost positive we didn't do series. I asked my friend who also went to my high school and he says the same thing. 


#7
Feb1512, 05:10 PM

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#8
Feb1512, 05:25 PM

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Also: about having a single answer field: are you doing an online course, or are the assignments given online? Unfortunately, in this Forum it happens over and over again that people submit correct solutions to online questions and are marked wrong. There are some genuine unsolved technical issues with designing robust online assigment marking schemes. RGV 


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