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

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The discussion centers on the expression (k+1)^2 in series calculations, with a participant questioning its validity. They argue that the terms should instead reflect (2k+1)^2 based on their backward summation from 2k+2. The confusion arises regarding the third to last term, which is presented as k^2, while they believe it should be 4k^2. The participant expresses a willingness to reconsider their reasoning if presented with a valid counterargument. The conversation highlights the complexities of series calculations and the need for clarity in mathematical expressions.
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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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