Geometric Series - I'm Stuck!!

knpoe03

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Apr 13, 2020
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Hello there! I've been struggling with this step (outlined in dark blue) on my Geometric Series worksheet. I'm thinking the answer is "no sum" but I'm not sure. Could someone please point me towards the right direction? EDIT: Figuratively, I mean. Not like "point me in the right direction of where I should go in this maze"
 

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I only saw a light blue one. In the future can you please post the problem instead of a link to the problem.
In the light blue problem, it is written as a geometric series where r=5/4 >1, so the sum goes towards infinity. Unless your teacher said to write no sum, I would say that the series diverges.
 
Of course, I will post a screenshot of the problem here:

Screenshot 2020-12-19 at 9.04.00 PM.png

I am confused about the dark blue outlined problem above. For reference, it is in the third vertical column and in the second horizontal row (count three to the left and two down). I've also found that it diverges, but there is no option for this in the "maze." So, I'm wondering if a) they want the answer to be no sum or b) I've messed up somewhere along the way.

If I were to mess up, it most likely would be in the box below the dark blue one (third vertical column and in the second horizontal row). I'm hoping that someone with much more of a grasp on this concept than I can clarify these questions. Thanks!
 
If the series is in fact a geometric series then it does have a finite sum if | r | < 1.
 
Why are you having trouble with the problem? As per the forum's posting guideline you need to show us your work so we can see where you made any errors.
 
Are you counting columns from right to left?
No, from left to right. The problem looks like (I'll describe it since I don't know how to type equations on here) a large E with an infinity sign above it, n=7 underneath the E, 1/2 next to the E, 5/4 multiplied by the 1/2, and superscript of n-1 to the right of the 5/4.

Why are you having trouble with the problem? As per the forum's posting guideline you need to show us your work so we can see where you made any errors.
The work for all of them are in the margins. However, I haven't begun writing out my work for the dark blue problem because I'm incredibly unsure of what the worksheet is expecting of me. If I come up with the answer that it diverges, does the worksheet want me to say no sum? Does a diverging series have no sum? Have I messed up on the previous question?

These are more of what I am concerned about. Really, I just need to be pointed in the right direction, either by explanations or links to resources that would help me understand the concept. It's difficult to write out my work whenever I am very lost and haven't a clue of where to go about performing this problem.
 
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If I start at the left how can I count three to the left and two down
 
If I start at the left how can I count three to the left and two down
This is quite embarrassing, I've mixed up my left and right. Whenever I said left I meant right, and vice versa. However, I believe I've solved it. I don't know if this is completely correct or not, though.
 
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