- #1
skyturnred
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Homework Statement
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]
Homework Equations
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=1-1+1-1+1+...(-1)[itex]^{n-1}[/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.