Quick Q: Understanding (k+1)^2 in Series Calculations

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Homework Help Overview

The discussion revolves around the expression (k+1)^2 in the context of series calculations, specifically examining the terms involved when summing up to 2k+2. Participants are trying to clarify the correct representation of terms in the series.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the reasoning behind the terms in the series, questioning whether (k+1)^2 is accurate or if it should be (2k+1)^2. There is a focus on the backward calculation of terms and the implications of different interpretations of the series.

Discussion Status

The discussion is active, with participants sharing their reasoning and questioning the assumptions made about the terms in the series. Some guidance has been offered, but there is no explicit consensus on the correct interpretation of the terms.

Contextual Notes

There appears to be confusion regarding the representation of the third to last term, with differing views on whether it should be k^2 or 4k^2. This discrepancy highlights the need for further clarification on the series setup.

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Should the highlighted part not be (k+1)^2, could anyone explain?>
 
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Well, it makes sense to me that it would be (2k+1)^2. Since you're summing up to 2k+2, going backwards from the final term you would have (2k+2)^2 then (2k+2 - 1)^2 then (2k+2 - 2)^2, etc. which would make the second to last term (2k+1)^2 and not (k+1)^2. What doesn't make sense to me is that it shows the third to last term as k^2. Using the same method I just described, which I don't see a problem with, you get that the third to last term should be (2k+2 - 2)^2 = (2k)^2 = 4k^2. So, either there's a mistake or I'm missing something. If my reasoning is correct, though, it explains why it's (2k+1)^2
 
elvishatcher said:
Well, it makes sense to me that it would be (2k+1)^2. Since you're summing up to 2k+2, going backwards from the final term you would have (2k+2)^2 then (2k+2 - 1)^2 then (2k+2 - 2)^2, etc. which would make the second to last term (2k+1)^2 and not (k+1)^2. What doesn't make sense to me is that it shows the third to last term as k^2. Using the same method I just described, which I don't see a problem with, you get that the third to last term should be (2k+2 - 2)^2 = (2k)^2 = 4k^2. So, either there's a mistake or I'm missing something. If my reasoning is correct, though, it explains why it's (2k+1)^2

That makes sense, thanks.
 
Glad I could help - if you ever figure out some reason why I'm wrong and it should be k^2 not 4k^2, let me know
 

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